If $P = a^{2} - 2 a b + b^{2}$ and $q = 4 a b,$ then $p + q a$ is:

(a - b)^{2} + 4 a^{2} b

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(a - b)^{2} - 4 a^{2} b

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(a - b)^{2} - 4 b a

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(a - b)^{2} - 4 b^{2} a

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Solution

The correct option is A $(a - b)^{2} + 4 a^{2} b$ .
It is given that $p = a^{2} - 2 a b + b^{2}$ and $q = 4 a b$ , then $p + q a$ will be as follows:

$p + q a = (a^{2} - 2 a b + b^{2}) + a (4 a b) = (a - b)^{2} + 4 a^{2} b (∵ (x - y)^{2} = x^{2} + y^{2} - 2 x y)$

Hence, $p + q a = (a - b)^{2} + 4 a^{2} b$ .

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Similar questions

Q. If P = a² − b² + 2ab, Q = a² + 4b² − 6ab, R = b² + b, S = a² − 4ab and T = −2a² + b² − ab + a. Find P + Q + R + S − T.

If $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ then what is the value of $a^{2} + b^{2}$

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Find:
$(a + b + c) \times (a + b - c) =$

Q. Question 3

Which of the following is correct?
a)

(a - b)^{2} = a^{2} + 2 a b - b^{2}

(a - b)^{2} = a^{2} - 2 a b + b^{2}

(a - b)^{2} = a^{2} - b^{2}

(a + b)^{2} = a^{2} + 2 a b - b^{2}

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If P=a2−2ab+b2 and q=4ab, then p+qa is:

The correct option is A (a−b)2+4a2b.It is given that p=a2−2ab+b2 and q=4ab, then p+qa will be as follows:p+qa=(a2−2ab+b2)+a(4ab)=(a−b)2+4a2b(∵(x−y)2=x2+y2−2xy)Hence, p+qa=(a−b)2+4a2b.

If $P = a^{2} - 2 a b + b^{2}$ and $q = 4 a b,$ then $p + q a$ is: