Question

25s^2+16w^2-u^2-40sw factorise

Answer 1

To factorize:

$25s^2+16w^2-u^2-40sw$

First of all, let us separate the terms containing $s, w$ on one side and $u$ on other side and let us try to make whole square in the terms of $s, w$.

$[25s^2+16w^2-40sw] -u^2 \\\Rightarrow [(5s)^2+(4w)^2-2 \times 5s\times 4w] -u^2$

Using the formula:

$a^2+b^2-2\times a \times b = (a-b)^2$

The given expression becomes:

$(5s-4w)^2-u^2$

Using the formula:

$a^2-b^2 = (a-b)(a+b)$

The given expression becomes:

$(5s-4w-u) (5s-4w+u)$

Therefore the factorized expression of $25s^2+16w^2-u^2-40sw$ is $(5s-4w-u) (5s-4w+u)$.