Evaluate-4 p q-3 q2-4 p q-3 q2A- 48 p 2 qB- 48 pq 2C- 48 p 2 q 2D- 48 pq

The correct option is B 48pq^2(4pq+3q)^2 (4pq 3q)^2 =(4pq)^2+2× 4pq× 3q+(3q)^2 [(4pq)^2 2× 4pq× 3q+(3q)^2] [Using identities (a+b)^2 =a^2+2ab+b^2 and (a ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identity 4

Evaluate:4 p ...

Question

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

48 p q^{2}

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48 p^{2} q

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48 p^{2} q^{2}

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48 p q

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Solution

The correct option is A $48 p q^{2}$
$(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2}$
$= (4 p q)^{2} + 2 \times 4 p q \times 3 q + (3 q)^{2} - [(4 p q)^{2} - 2 \times 4 p q \times 3 q + (3 q)^{2}]$
$[U s i n g i d e n t i t i e s (a + b)^{2} = a^{2} + 2 a b + b^{2} a n d (a - b) 62 = a 62 - 2 a b + b^{2}]$
$= 16 p^{2} q^{2} + 24 p q^{2} + 9 q^{2} - [16 p^{2} q^{2} - 24 p q^{2} + 9 q^{2}]$ $= 16 p^{2} q^{2} + 24 p q^{2} + 9 q^{2} - 16 p^{2} q^{2} + 24 p q^{2} - 9 q^{2}$
$= 48 p q^{2}$

Suggest Corrections

Evaluate: (4pq+3q)2−(4pq−3q)2

The correct option is A 48pq2(4pq+3q)2−(4pq−3q)2 =(4pq)2+2×4pq×3q+(3q)2−[(4pq)2−2×4pq×3q+(3q)2] [Using identities (a+b)2=a2+2ab+b2 and (a−b)62=a62−2ab+b2] =16p2q2+24pq2+9q2−[16p2q2−24pq2+9q2] =16p2q2+24pq2+9q2−16p2q2+24pq2−9q2 =48pq2

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