2-(3*x-7)/4*x+(3*x-5*y)/8*x simplified Step-by-Step Math Problem Solver

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Created on: 2011-11-23

2−3x−74x+3x−5y8x

We need to perform a multiplication.

The following rule is applied:

ABC=ACB

In our example, the factors in the new numerator are:

(3x−7), x,

Notice that all non-fraction factors are placed in the numerator.

The only factor in the new denominator is:

We need to perform a multiplication.

The following rule is applied:

ABC=ACB

In our example, the factors in the new numerator are:

(3x−5y), x,

Notice that all non-fraction factors are placed in the numerator.

The only factor in the new denominator is:

2−(3x−7)x4+(3x−5y)x8

Simple numerical terms are commonly written last.

−(3x−7)x4+(3x−5y)x8+2

We need to add fractions.

The following rule is applied:

AB+CD=LCDBA+LCDDCLCD

This example involves 3 terms.

Note that 1 non-fractional terms are treated as fractions with denominator equal to 1.

The LCD is equal to:

4·8

8(−(3x−7)x)+4((3x−5y)x)+(4·8)24·8

We need to get rid of parentheses in this term.

All the negative factors will change sign.

In our example, we have only one negative factor.

The sign of the term will change, since there is an odd number of negative factors.

We need to get rid of parentheses in this term.

All the negative factors will change sign.

In our example, we do not have any negative factors.

The sign of the term will not change.

Numerical factors in this term have been multiplied.

−8(3x−7)x+4(3x−5y)x+32·24·8

Numerical factors in this term have been multiplied.

−8(3x−7)x+4(3x−5y)x+644·8

We need to arrange this term for expansion.

Commonly, the non-expandable factor is written first.

In our example, the factor is 8x.

We need to arrange this term for expansion.

Commonly, the non-expandable factor is written first.

In our example, the factor is 4x.

−(8x)(3x−7)+(4x)(3x−5y)+644·8

We need to expand this term by multiplying a term and an expression.

The following product distributive property will be used:

A(B+C)=AB+AC.

In our example, the resulting expression will consist of 2 terms:

the first term is a product of 8x and 3x.

the second term is a product of 8x and −7.

We need to expand this term by multiplying a term and an expression.

The following product distributive property will be used:

A(B+C)=AB+AC.

In our example, the resulting expression will consist of 2 terms:

the first term is a product of 4x and 3x.

the second term is a product of 4x and −5y.

−(8x·3x+8x(−7))+(4x·3x−4x·5y)+644·8

We need to organize this term into groups of like factors, so we can combine them easier.

Numerical terms are commonly written first.

The following are like factors:

x, x

We need to get rid of parentheses in this term.

All the negative factors will change sign.

In our example, we have only one negative factor.

The sign of the term will change, since there is an odd number of negative factors.

We need to organize this term into groups of like factors, so we can combine them easier.

Numerical terms are commonly written first.

The following are like factors:

x, x

Numerical terms are commonly written first.

−(8·3xx−8x·7)+(4·3xx−4·5xy)+644·8

We need to combine like factors in this term by adding up all the exponents and copying the base.

No exponent implies the value of 1.

Numerical factors will be multiplied.

The following are like factors:

x, x

Numerical terms are commonly written first.

We need to combine like factors in this term by adding up all the exponents and copying the base.

No exponent implies the value of 1.

Numerical factors will be multiplied.

The following are like factors:

x, x

Numerical factors in this term have been multiplied.

−(24x¹⁺¹−8·7x)+(12x¹⁺¹−20xy)+644·8

Numerical terms in this expression have been added.

Numerical factors in this term have been multiplied.

Numerical terms in this expression have been added.

−(24x²−56x)+(12x²−20xy)+644·8

We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, the following 2 terms will change sign:

24x², −56x

−24x²+56x+12x²−20xy+644·8

We need to organize this expression into groups of like terms, so we can combine them easier.

There is only one group of like terms:

−24x², 12x²

−24x²+12x²+56x−20xy+644·8

We need to combine like terms in this expression by adding up all numerical coefficients and copying the literal part, if any.

No numerical coefficient implies value of 1.

There is only one group of like terms:

−24x², 12x²

−12x²+56x−20xy+644·8

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

In our example,

Prime number 2 to the power of 2 equals 4.

Prime number 3 to the power of 1 equals 3.

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

In our example,

Prime number 2 to the power of 6 equals 64.

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

In our example,

Prime number 2 to the power of 3 equals 8.

Prime number 7 to the power of 1 equals 7.

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

In our example,

Prime number 2 to the power of 2 equals 4.

Prime number 5 to the power of 1 equals 5.

−2²·3x²+(2³·7)x−(2²·5)xy+2⁶4·8

We need to factor the GCF (Greatest Common Factor).

The resulting term is a product of the GCF and the original expression divided by the GCF.

In our example, the GCF is equal to 2².

2²(−2²·3x²2²+2³·7x2²−2²·5xy2²+2⁶2²)4·8

We need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, this is the common factor:

2².

We need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, this is the common factor:

2².

We need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, this is the common factor:

2².

We need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, this is the common factor:

2².

2²(−1·3x²1+2³⁻²·7x1−1·5xy1+2⁶⁻²1)4·8

Number 1 as a factor, does not need to be explicitly written.

In other words: 1A=A.

In our example, the above transformation has been applied once.

Numerical terms in this expression have been added.

Number 1 as a factor, does not need to be explicitly written.

In other words: 1A=A.

In our example, the above transformation has been applied once.

Numerical terms in this expression have been added.

2²(−3x²1+2¹·7x1−5xy1+2⁴1)4·8

Any fraction which has its denominator equal to 1 is equal to its numerator.

In other words:

NUM1=NUM

In our example, the numerator is equal to 3x².

This is a special case of exponentiation.

The following rule is applied:

A¹=A

In our example,

A is equal to 2.

Any fraction which has its denominator equal to 1 is equal to its numerator.

In other words:

NUM1=NUM

In our example, the numerator is equal to 5xy.

Any fraction which has its denominator equal to 1 is equal to its numerator.

In other words:

NUM1=NUM

In our example, the numerator is equal to 2⁴.

2²(−(3x²)+2·7x1−(5xy)+2⁴)4·8

We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, the following 2 terms will change sign:

3, x²

Any fraction which has its denominator equal to 1 is equal to its numerator.

In other words:

NUM1=NUM

In our example, the numerator is equal to 2·7x.

We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, the following 3 terms will change sign:

5, x, y

We need to evaluate a power by multiplying the base by itself as many times as the exponent indicates.

In our example, base 2 will be multiplied by itself four times.

2²(−3x²+2·7x−5xy+16)4·8

Numerical factors in this term have been multiplied.

2²(−3x²+14x−5xy+16)4·8

We need to evaluate a power by multiplying the base by itself as many times as the exponent indicates.

In our example, base 2 will be multiplied by itself twice.

Numerical factors in this term have been multiplied.

4(−3x²+14x−5xy+16)32

We can reduce this fraction by dividing both numerator and denominator by a common numeric factors.

In our example,

both number 4 in numerator and number 32 in denominator are divisible by 4.

1(−3x²+14x−5xy+16)8

Number 1 as a factor, does not need to be explicitly written.

In other words: 1A=A.

In our example, the above transformation has been applied once.

−3x²+14x−5xy+168

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