Question

Factorise : ${(ax+by)}^2+{(2bx-2ay)}^2-6abxy$

• A. $a^2{x}^2+b^2{y}^2+2b^2{x}^2+2a^2{y}^2+6abxy$
• B. $a^2{x}^2+b^2{y}^2+4b^2{x}^2+4a^2{y}^2-12abxy$
• C. $a^2{x}^2+b^2{y}^2+b^2{x}^2+a^2{y}^2+4abxy$
• D. $a^2{x}^2+b^2{y}^2+4b^2{x}^2+4a^2{y}^2+6abxy$

Answer 1

The correct option is B $a^2{x}^2+b^2{y}^2+4b^2{x}^2+4a^2{y}^2-12abxy$

${(ax+by)}^2+{(2bx-2ay)}^2-babxy$

Here we will use the following identity,

$\Rightarrow {(m+n)}^2=m^2+n^2+2mn$

and ${(m-n)}^2=m^2+n^2-2mn$

Using this we have :

$={\left(ax\right)}^2+{\left(by\right)}^2+2axby+4{\left(bx\right)}^2+4{\left(ay\right)}^2-8axby-6abxy$

$=a^2{x}^2+b^2{y}^2+4b^2{x}^2+4a^2{y}^2-14axby+2axby$

$=a^2{x}^2+b^2{y}^2+4b^2{x}^2+4a^2{y}^2-12axby$

Hence, the answer is $a^2{x}^2+b^2{y}^2+4b^2{x}^2+4a^2{y}^2-12axby.$