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

Answer:

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

Step-by-step 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:

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