Question

(a) $(a-b)^2+4 a b$ (b) $a(a+b)+b(a+b)$ (c) $\left(a^2-b^2\right)+2 b(b+a)$ (d) $(a-b) b+(a+b) 2 b$ (e) $(a+b)^2-2 a(a-b)+a(2 a-2 b)$

   (a) $(a-b)^2+4 a b$
(b) $a(a+b)+b(a+b)$
(c) $\left(a^2-b^2\right)+2 b(b+a)$
(d) $(a-b) b+(a+b) 2 b$
(e) $(a+b)^2-2 a(a-b)+a(2 a-2 b)$

The Pearson Guide to Objective Arithmetic for Competitive Examinations

The Pearson Guide to Objective Arithmetic for Competitive Examinations

Dinesh Khattar 2nd Edition

Chapter 33, Problem 22

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Step 1

We can expand \((a-b)^2\) using the formula \((x-y)^2 = x^2 - 2xy + y^2\): \[ (a-b)^2 = a^2 - 2ab + b^2 \] Now, substituting this back into the expression gives: \[ a^2 - 2ab + b^2 + 4ab = a^2 + 2ab + b^2 \] Next, we recognize that \(a^2 + 2ab + b^2\) is a perfect Show more…

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(a) $(a-b)^2+4 a b$ (b) $a(a+b)+b(a+b)$ (c) $\left(a^2-b^2\right)+2 b(b+a)$ (d) $(a-b) b+(a+b) 2 b$ (e) $(a+b)^2-2 a(a-b)+a(2 a-2 b)$

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