Question

Factor the expression

by filling in the blank

Answer 1

After factoring we get:

`(\mathbf{2}q^2r+\mathbf{3}s^2t)(\mathbf{4}q^4r^2-\mathbf{6}q^2rs^2t+\mathbf{9}s^4t^2)`

Explanation:

The expression given is:

`8q^6r^3+27s^6t^3`

We need to factor the expression using the formula:

`a^3+b^3=(a+b)(a^2-ab+b^2)`

Given the expression:

we have

`a = 2q^2r\\b= 3s^2t`

Now applying the formula:
`a^3+b^3=(a+b)(a^2-ab+b^2)`

`(2q^2r)^3+(3s^2t)^3\\=(2q^2r+3s^2t)((2q^2r)^2-(2q^2r)(3s^2t)+(3s^2t)^2)\\=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)`

So, after factoring we get:

`(\mathbf{2}q^2r+\mathbf{3}s^2t)(\mathbf{4}q^4r^2-\mathbf{6}q^2rs^2t+\mathbf{9}s^4t^2)`