Question

The expression $(2x-5y{)}^2$ is equal to

• A. $4x^2-20xy-25y^2$
• B. $4x^2-20xy+15y^2$
• C. $4x^2-20xy+25y^2$
• D. $4x^2-10xy+25y^2$

Answer 1

The correct option is C $4x^2-20xy+25y^2$

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

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

$(2x-5y{)}^2=(2x-5y\left)\right(2x-5y)$
$=\left(2x\right)(2x-5y)+(-5y)(2x-5y)$
$=\left(2x\right)\left(2x\right)-\left(2x\right)\left(5y\right)+(-5y)\left(2x\right)+(-5y)(-5y)$
$=(2x{)}^2+2(2x\left)\right(-5y)+(-5y{)}^2$
$=4x^2+2\left(2x\right)(-5y)+25y^2$
$=4x^2-20xy+25y^2$

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

$(2x-5y{)}^2$
$=(2x{)}^2+2(2x\left)\right(-5y)+(-5y{)}^2$
$=4x^2+2\left(2x\right)(-5y)+25y^2$
$=4x^2-20xy+25y^2$