Simplify the following algebraic expression- 9 pq -6 r 2-108 pqr A- 81 p 2 q 2-18 r 2B- 81 p2 q2-36 r2C- 81 p 2 q 2-36 r 2-216 pqrD- 81 p 2 q 2-18 r 2-54 pqr

The correct option is B 81p^2q^2 nbsp;+ 36r^2 Given: nbsp;(9pq + 6r)^2 nbsp; 108 pqr nbsp; Expand (9pq + 6r)^2 nbsp;using the identity,(a + b)^2 n ...

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Standard VIII

Mathematics

Algebraic Identity: (a + b)^2 = a^2 + b^2 + 2ab

Simplify the ...

Question

Simplify the following algebraic expression: $(9 p q + 6 r)^{2} - 108 p q r$

$81 p^{2} q^{2} + 18 r^{2}$

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$81 p^{2} q^{2} + 36 r^{2}$

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$81 p^{2} q^{2} + 36 r^{2} - 216 p q r$

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$81 p^{2} q^{2} + 18 r^{2} - 54 p q r$

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Solution

The correct option is B: $81 p^{2} q^{2} + 36 r^{2}$
Given: $(9 p q + 6 r)^{2} - 108 p q r$
$= (9 p q)^{2} + 2 \times 9 p q \times 6 r + (6 r)^{2} - 108 p q r$
$= 81 (p)^{2} (q)^{2} + 108 p q r + 36 (r)^{2} - 108 p q r$ [Using the identity, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ]
$= 81 p^{2} q^{2} + 36 r^{2}$

Suggest Corrections

Simplify the following algebraic expression: (9pq+6r)2−108pqr

The correct option is B: 81p2q2+36r2Given: (9pq+6r)2−108pqr =(9pq)2+2×9pq×6r+(6r)2−108pqr=81(p)2(q)2+108pqr+36(r)2−108pqr [Using the identity,(a+b)2=a2+2ab+b2]=81p2q2+36r2

Simplify the following algebraic expression: $(9 p q + 6 r)^{2} - 108 p q r$