By applying (a+b)^2=a^2+2ab+b^2, and (a b)^2=a^2 2ab+b^2 in the given expression, we get, nbsp; (4pq + 3q)^2 (4pq 3q)^2 = [(4pq)^2 nbsp;+ (3q)^2 nbsp;+ ...

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Standard VIII

Mathematics

Addition and Subtraction of Polynomials

4pq+3q2−4pq−3...

Question

(4pq+3q)2−(4pq−3q)2 =

44 p q^{2}

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48 p^{2} q

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48 p q^{2}

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44 p^{2} q

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Solution

The correct option is C $48 p q^{2}$
By applying $(a + b)^{2} = a^{2} + 2 a b + b^{2},$ and $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ in the given expression, we get,

${(4 p q + 3 q)}^{2} - {(4 p q - 3 q)}^{2}$
$= [{(4 p q)}^{2} + {(3 q)}^{2} + 2 (4 p q) (3 q)]$
$- [{(4 p q)}^{2} + {(3 q)}^{2} - 2 (4 p q) (3 q)]$
On simplifying, we get,
$= 24 p q^{2} + 24 p q^{2}$
$= 48 p q^{2}$

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Similar questions

Q. (4pq+3q)2−(4pq−3q)2 =

Prove that: $(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}$ .

Show that:

$(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}$

Q. The value of

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

Q. Question 5(iv)
Show that:

(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}

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(4pq+3q)2−(4pq−3q)2 =

The correct option is C 48pq2By applying (a+b)2=a2+2ab+b2, and (a−b)2=a2−2ab+b2 in the given expression, we get, (4pq+3q)2−(4pq−3q)2 =[(4pq)2+(3q)2+2(4pq)(3q)] −[(4pq)2+(3q)2−2(4pq)(3q)] On simplifying, we get, =24pq2+24pq2 =48pq2