to factorize the expression 22 − 7xy - 2x2y2.

Question

ScanSolve AI Tutor · Accepted Answer

I will solve question 7(a) from the image.

The question asks to factorize the expression $22 - 7xy - 2x^2y^2$ .

Identify the coefficients.
This is a quadratic expression in terms of $xy$ . Let $u = xy$ . The expression becomes $22 - 7u - 2u^2$ .
We need to find two numbers that multiply to the product of the constant term and the coefficient of $u^2$ , which is $22 \times (-2) = -44$ . These two numbers must also add up to the coefficient of $u$ , which is $-7$ .
Find two numbers that multiply to $-44$ and add to $-7$ .
The two numbers are 4 and $-11$ . ( $4 \times -11 = -44$ and $4 + (-11) = -7$ ).
Rewrite the middle term using these two numbers.
Substitute $xy$ back into the expression:
$22 - 7xy - 2x^2y^2 = 22 + 4xy - 11xy - 2x^2y^2$
Factor by grouping.
Group the terms and factor out the common factors from each group.
$(22 + 4xy) - (11xy + 2x^2y^2)$
Factor 2 from the first group and $xy$ from the second group. Note that we factor out $xy$ and not $11xy$ or $2x^2y^2$ to get a common binomial factor.
$2(11 + 2xy) - xy(11 + 2xy)$
Factor out the common binomial.
$(11 + 2xy)(2 - xy)$
The factored form of $22 - 7xy - 2x^2y^2$ is $(11 + 2xy)(2 - xy)$ .

To factorize the expression 22 - 7xy - 2x2y2.