Question

The expression $(4a+3b{)}^2$ is equal to

• A. $6a^2+24ab+9b^2$
• B. $16a^2+24ab+9b^2$
• C. $16a^2+4ab+9b^2$
• D. $16a^2+14ab+9b^2$

Answer 1

The correct option is B $16a^2+24ab+9b^2$

$\underset{–}{ConceptInvolved}$:
$(a+b{)}^2=a^2+2ab+b^2$

$\underset{–}{Method}$:
Using the FOIL rule.
F=First term, O= Outside term, I = Inside term, L= Last term.

$(4a+3b{)}^2=(4a+3b\left)\right(4a+3b)$
$=\left(4a\right)(4a+3b)+\left(3b\right)(4a+3b)$
$=\left(4a\right)\left(4a\right)+\left(4a\right)\left(3b\right)+\left(3b\right)\left(4a\right)+\left(3b\right)\left(3b\right)$
$=(4a{)}^2+2(4a\left)\right(3b)+(3b{)}^2$
$=16a^2+2\left(4a\right)\left(3b\right)+9b^2$
$=16a^2+24ab+9b^2$

This is the required expression obtained using FOIL rule.
Also, we can use the identity
$(a+b{)}^2=a^2+2ab+b^2$.

$(4a+3b{)}^2$
$=(4a{)}^2+2(4a\left)\right(3b)+(3b{)}^2$
$=16a^2+2\left(4a\right)\left(3b\right)+9b^2$
$=16a^2+24ab+9b^2$