Question

25x2 −36y 8 25, x, squared, minus, 36, y, start superscript, 8, end superscript We can factor the expression as (U+V)(U-V)(U+V)(U−V)left parenthesis, U, plus, V, right parenthesis, left parenthesis, U, minus, V, right parenthesis where UUU and VVV are either constant integers or single-variable expressions. What are UUU and VVV?

Answer 1

`(5x + 6y^4)(5x - 6y^4)`

Explanation:

Given the expression:

`25x^2 -36y^8`

We are to express it as difference of two square (u+v)(u-v). According to the rule:

`u^2 - v^2 = (u+v)(u-v)`

We need to express
`25x^2 -36y^8` as difference of squares and this is as shown:

`= 25x^2 -36y^8\\= 5^2x^2 - 6^2(y^4)^2\\= (5x)^2 -(6y^4)^2\\`

From the resulting expression we can say:

`u = 5x \ and \ v = 6y^4`

If we substitute in the rule above we will have:

`= (5x)^2 -(6y^4)^2\\= (5x + 6y^4)(5x - 6y^4)`

Hence the expression expressed as difference of two square is:

`(5x + 6y^4)(5x - 6y^4)`