Question

2. What is the product of (x+a) and (x+b)?
L.x2+ (a-b)X + ab ll. x2 + (a+b)x - ab
JII. x2 + (a+b)x - ab IV. x2 + (a+b)x + ab
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Answer 1

We will discuss here about the expansion of (x ± a)(x ± b)

(x + a)(x + b) = x(x + b) + a (x + b)

= x2 + xb + ax + ab

= x2 + (b + a)x + ab

(x - a)(x - b) = x(x - b) - a (x - b)

= x2 - xb - ax + ab

= x2 - (b + a)x + ab

x + a)(x - b) = x(x - b) + a (x - b)

= x2 - xb + ax - ab

= x2 + (a - b)x - ab

(x - a)(x + b) = x(x + b) - a (x + b)

= x2 + xb - ax - ab

= x2 - (a - b)x – ab

Thus, we have

(x + a)(x + b) = x2 + (b + a)x + ab

(x - a)(x - b) = x2 - (b + a)x + ab

(x + a)(x - b) = x2 + (a - b)x - ab

(x - a)(x + b) = x2 - (a - b)x – ab

Answer 2

$\huge\rm\purple{an{\mathcal{S}}wer:}$

${}$

$\bf{{\underline{To~find}}:}$

• The product of $\sf{(x+a)}$ and $\sf{(x+b)}$

$\bf{{\underline{Solution}}:}$

$\tt{~~~~~~~~(x+a)(x+b)}$

$\tt{:\longmapsto (x~×~x)+(x×b)+(a×x)+(a×b)}$

$\tt{:\longmapsto x^{2}+(bx+ax)+ab}$

$\tt{:\longmapsto {\purple{\underline{\boxed{\bf x^{2}+(a+b)x+ab}}}}}$

$\bf{{\underline{Required~answer}}:}$

$\tt (x + a)(x + b) = \purple{ \underline{ \boxed{ \bf {x}^{2} + (a + b)x + ab}}}$

$\tt(IV) \: \: \purple{ \bf {x}^{2} + (a + b)x + ab}$