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Types of Expressions Based on the Number of Terms

Solve: ax + ...

Question

Solve:
$a (x + y) + b (x - y) = a^{2} - a b + b^{2}$
$a (x + y) - b (x - y) = a^{2} + a b + b^{2}$

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Solution

$a (x + y) + b (x - y) = a^{2} - a b + b^{2}$
$a (x + y) - b (x - y) = a^{2} + a b + b^{2}$
Let $x + y = X$ , $x - y = Y$
$a X + b Y = a^{2} - a b + b^{2}$ ……….(i)
$a X - b Y = a^{2} + a b + b^{2}$ ………(ii)
Adding (i) & (ii)
$a x = 2 (a^{2} + b^{2})$
$X = \frac{a^{2} + b^{2}}{a}$ ,
$Y = - a$
$x + y = \frac{a^{2} + b^{2}}{a} = a + \frac{b^{2}}{a}$ ……..(iii)
$x - y = - a$ ………(iv)
Adding (iii) & (iv)
$2 x = \frac{b^{2}}{a}$
$x = \frac{b^{2}}{2 a}$ ,
$y = \frac{b^{2}}{2 a} + a$ .

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