Factorise the following completely: 1) 10×2 - 9xy + 2y2, 2) 5×2 + 18xy + 9y2

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to factorize the given expressions:

1) Factorize $10x^2 - 9xy + 2y^2$

Find two numbers that multiply to $10 \times 2 = 20$ and add up to $-9$ .
These numbers are $-4$ and $-5$ . Rewrite the middle term using these numbers.
$10x^2 - 9xy + 2y^2 = 10x^2 - 5xy - 4xy + 2y^2$
Group the terms and factor out the common factors from each group.
$(10x^2 - 5xy) - (4xy - 2y^2)$ $5x(2x - y) - 2y(2x - y)$
Factor out the common binomial $(2x - y)$ .
$(5x - 2y)(2x - y)$
The factored expression is $\boxed{(5x - 2y)(2x - y)}$ .

2) Factorize $5x^2 + 18xy + 9y^2$
Find two numbers that multiply to $5 \times 9 = 45$ and add up to 18.
These numbers are 3 and 15. Rewrite the middle term using these numbers.
$5x^2 + 18xy + 9y^2 = 5x^2 + 3xy + 15xy + 9y^2$
Group the terms and factor out the common factors from each group.
$(5x^2 + 3xy) + (15xy + 9y^2)$ $x(5x + 3y) + 3y(5x + 3y)$
Factor out the common binomial $(5x + 3y)$ .
$(x + 3y)(5x + 3y)$
The factored expression is $\boxed{(x + 3y)(5x + 3y)}$ .

Factorise the following completely: 1) 10x2 - 9xy + 2y2, 2) 5x2 + 18xy + 9y2