Question

Factorise $9(p-q{)}^2-4(2p+q{)}^2$

• A. $-(7p-q)(p+5q)$
• B. $(7p-q)(p+5q)$
• C. $-(7p+q)(p+5q)$
• D. $(7p+q)(p-5q)$

Answer 1

The correct option is A $-(7p-q)(p+5q)$

$9{(p-q)}^2-4{(2p+q)}^2$

$={3(p-q)}^2-{2(2p+q)}^2$ is of the form $a^2-b^2=(a-b)(a+b)$

$={(3p-3q)}^2-{(4p+2q)}^2$

$=(3p-3q+4p+2q)(3p-3q-4p-2q)$

$=(7p-q)(-p-5q)$

$=-(7p-q)(p+5q)$