Question

to verify algebraic identity a2-b2=(a+b)(a-b)

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO VERIFY

The algebraic identity

$\sf{ {a}^{2} - {b}^{2} = (a + b)(a - b )\: }$

CALCULATION

Let us take a = 10 and b = 7

LHS

$= \sf{ {a}^{2} - {b}^{2} \: }$

$= \sf{ {10}^{2} - {7}^{2} }\:$

$= \sf{ 100 - 49\: }$

$= \sf{ 51\: }$

RHS

$= \sf{(a + b)(a - b)} \:$

$= \sf{(10 + 7)(10- 7)} \:$

$= \sf{17 \times 3} \:$

$= \sf{51} \:$

Hence LHS = RHS

Hence Verified

NOTE : Above mentioned Identity can be verified using any other real number

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Answer 2

We have to verify algebraic identity: $a^{2}-b^{2}$ = (a + b)(a - b).

Solution:

R.H.S. = (a + b)(a - b)

Expanding the terms, we get

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

= $a^{2}$ - ab + ba - $b^{2}$

= $a^{2}-b^{2}$

= L.H.S., verified.

Thus, $a^{2}-b^{2}$ = (a + b)(a - b), the algebraic identity is verified.