How to multiply and divide like terms
Rules for multiplying like terms and dividing like terms
When multiplying like terms (terms with the same base) we’ll multiply the coefficients and add the exponents. For example,
???4x^2\cdot3x^5???
???4\cdot3 x^{2+5}???
???12x^7???
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When dividing like terms we’ll divide the coefficients and subtract the exponents. “Canceling” is a term often used instead of subtracting the exponents, but it means the same thing. For example,
???\frac{4x^3}{2x}???
???\frac{4}{2}x^{3-1}???
???2x^2???
How to combine like terms by multiplying and dividing
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Simplifying the expression by combining like terms
Example
Simplify the expression.
???\frac{x(x+2x-a+b)}{x}???
Notice that the ???x??? outside of the parentheses in the numerator is being multiplied by all the other terms in the numerator. Also notice that ???x??? is in the denominator which means we need to divide by ???x???. Since division undoes multiplication, we can cancel the ???x??? outside of parentheses with the ???x??? in the denominator.
???x+2x-a+b???
Combine like terms (the ???x??? terms in this case).
???(1+2)x-a+b???
???3x-a+b???
Let’s try another example of multiplying and dividing like terms.
“Canceling” is a term often used instead of subtracting the exponents, but it means the same thing.
Example
Simplify the expression.
???\frac{(2x-4)(x^2-x+3)}{2}???
Start by expanding the numerator.
???\frac{2x^3-2x^2+6x-4x^2+4x-12}{2}???
Combine like terms in the numerator. Remember to group variables with the same exponents together.
???\frac{2x^3-2x^2-4x^2+6x+4x-12}{2}???
???\frac{2x^3-6x^2+10x-12}{2}???
Since every term in the numerator is even and ???2??? is in the denominator we can divide every term on top by ???2???.
???x^3-3x^2+5x-6???
