State whether the following statement is true or false:
${(2 p - 3 q)}^{2}$ = $4 p^{2} + 9 q^{2} - 12 p q$

True

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False

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Solution

The correct option is A True
$(2 p - 3 q)^{2} = 4 p^{2} + 9 q^{2} - 12 p q$

$L . H . S = (2 p - 3 q)^{2}$

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

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

$= 4 p^{2} - 6 p q - 6 p q + 9 q^{2}$

$= 4 p^{2} + 9 q^{2} - 12 p q$

$= R . H . S$

$∴$ $(2 p - 3 q)^{2} = 4 p^{2} + 9 q^{2} - 12 p q$

Suggest Corrections

Similar questions

\frac{12 p q}{(2 p + 3 q)^{2} - (2 p - 3 q)^{2}}

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

Question 38

State whether the statement given is True or False.

Sum of 2 and p is 2p.

∠ A O C = ∠ D O B

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