Factor out common factor

Question

Factor out the indicated common factor of the expression. Then completely factor the expression.

x^10/3 -9x^4/3;x^4/3

Answer 1

Step 1: Factor out the common factor (x^4/3) of the equation [One way to think of it is to take out the common factor or multiply the equation by 1 or divide the equation by the factor]

(x^4/3 / x^4/3)(x^10/3 - 9x^4/3) = x^4/3 (x^10/3/ x^4/3- 9x^4/3/x^4/3) = x^4/3 (x^(10-4)/3- 9x^(4-4)/3) = x^4/3 (x²-9)

Ans: x^4/3 (x²-9)

Step 2: Completely factor the expression [Notice there is another expression that can be factored down, which is also called a difference of two perfect squares]

To solve the difference of two perfect squares which in this case is x² and 9, just split them and assign a positive and negative. To check, you can multiply it out and check that (a+b)(a-b) = a²-b².

x^4/3 (x²-9) = x^4/3 (x+3)(x-3)

Ans: x^4/3 (x+3)(x-3)