how would i factor this
2x^2(p + q^3) - (p + q^3)
isn't (p+q^3) a common factor? so ..
2x^2(p + q^3) - (p + q^3)
= (p+q^3)(2x^2 - 1)
if you are restricted to rational coefficients, you are done, if not you could say
=(p+q^3)(√2x - 1)(√2x + 1)
9x^2-27y^2
To factor the given expression 2x^2(p + q^3) - (p + q^3), we can look for common factors and use the distributive property of multiplication over addition/subtraction.
Step 1: Take out the common factor
We notice that both terms in the expression have a common factor of (p + q^3). So, we can factor it out.
2x^2(p + q^3) - (p + q^3) = (p + q^3)(2x^2 - 1)
Step 2: Simplify if needed
If the expression inside the parentheses can be simplified further, do so. In this case, it can't be simplified any further, so we can consider our factored form complete.
Therefore, the factored form of 2x^2(p + q^3) - (p + q^3) is (p + q^3)(2x^2 - 1).