Question

The expression $(3p+q)\times (3p-q)$ would be equal to?

• A. $p^2-q^2$
• B. $p^2+q^2$
• C. $9p^2-q^2$
• D. $9p^2+3q^2$

Answer 1

The correct option is C $9p^2-q^2$

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

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

$(3p+q)\times (3p-q)$
$=(3p+q)(3p-q)$
$=\left(3p\right)(3p-q)+\left(q\right)(3p-q)$
$=\left(3p\right)\left(3p\right)+\left(3p\right)(-q)+\left(q\right)\left(3p\right)+\left(q\right)(-q)$
$=(3p{)}^2+(3p\left)\right(-q)+(q\left)\right(3p)+(q\left)\right(-q)$
$=9p^2-3pq+3pq-q^2$
$=9p^2+3pq-3pq-q^2$

$\because 3pq-3pq=0$

$\Rightarrow (3p+q)\times (3p-q)=9p^2-q^2$

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

$(3p+q)\times (3p-q)$
$=(3p{)}^2-(q{)}^2$
$=9p^2-q^2$