Question

Expand ${(4a–2b–3c)}^2$

• A. $16a^2-4b^2-9c^2-16ab+12bc-24ac$
• B. $16a^2+4b^2+9c^2+16ab+12bc+24ac$
• C. $16a^2+4b^2+9c^2-16ab+12bc+24ac$
• D. $16a^2+4b^2+9c^2-16ab+12bc-24ac$

Answer 1

The correct option is D

$16a^2+4b^2+9c^2-16ab+12bc-24ac$

We know that the expansion of the term ${(x+y+z)}^2$ is $x^2+y^2+z^2+2xy+2yz+2zx$

Comparing the terms to those given in the question, we get x = 4a, y = -2b, z = -3c

${(4a–2b–3c)}^2$ = ${\left(4a\right)}^2+{(-2b)}^2+{(-3c)}^2+2\left(4a\right)(-2b)+2(-2b)(-3c)+2(-3c)\left(4a\right)=16a^2+4b^2+9c^2-16ab+12bc-24ac$