Question 84 (xii)

Simplify

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

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Solution

We have, $(p q - q r)^{2} + 4 p q^{2} r$
$= p^{2} q^{2} + q^{2} r^{2} - 2 p q^{2} r + 4 p q^{2} r$ [using the identity, $(a - b)^{2} = a^{2} + b^{2} - 2 a b$ ]
$= p^{2} q^{2} + q^{2} r^{2} + 2 p q^{2} r$

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Question 84 (xii)

Simplify

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

Question 6
Angles Q and R of a $Δ$ PQR are $25^{\circ}$ and $65^{\circ}$ .
Write which of the following is true:
(i) $P Q^{2} + Q R^{2} = R P^{2}$
(ii) $P Q^{2} + R P^{2} = Q R^{2}$
(iii) $R P^{2} + Q R^{2} = P Q^{2}$

Q. Angles Q and R of a

Δ P Q R

are

25^{\circ} a n d 65^{\circ}

. Write which of the following is true:

\begin{matrix} (a) P Q^{2} + Q R^{2} = R P^{2} (b) P Q^{2} + R P^{2} = Q R^{2} (c) R P^{2} + Q R^{2} = P Q^{2} \end{matrix}

Q. Multiply:

[p^{2} + (q r)^{2}] [p^{2} - (q r)^{2}]

and evaluate for

p = 1, q = 2, r = 3

Question 58
${(\frac{5}{8})}^{9} \div {(\frac{5}{8})}^{4} = {(\frac{5}{8})}^{4}$

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

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Question 84 (xii) Simplify (pq−qr)2+4pq2r

We have, (pq−qr)2+4pq2r =p2q2+q2r2−2pq2r+4pq2r [using the identity, (a−b)2=a2+b2−2ab] =p2q2+q2r2+2pq2r

Question 84 (xii)

Simplify

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

We have, $(p q - q r)^{2} + 4 p q^{2} r$
$= p^{2} q^{2} + q^{2} r^{2} - 2 p q^{2} r + 4 p q^{2} r$ [using the identity, $(a - b)^{2} = a^{2} + b^{2} - 2 a b$ ]
$= p^{2} q^{2} + q^{2} r^{2} + 2 p q^{2} r$