Question

(a+1)^2-(b+1)^2 factorise
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Answer 1

Answer:

(a+b+2)(a-b)

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Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow (a+1)^2-(b+1)^2$

$\large\underline\bold{TO,}$

$\sf\large\dashrightarrow FACTORISE\:THE\:GIVEN\: EQUATION .$

✯IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: (a+b)^2=a^2+b^2+2ab\:\: \star}}}$

$\large{\boxed{\bf{ \star\:\: (a-b)^2=a^2+b^2-2ab\:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\implies \bigg( a^2+(1)^2+2(1)(a) \bigg) - \bigg( b^2+(1)^2-2(1)(b) \bigg)\:--\boxed{by\:given\: identity.}$

$\sf\implies a^2+\cancel{1}+2a-b^2-\cancel{1}-2b$

$\sf\implies a^2+2a-b^2-2b$

$\sf\implies a^2+b^2+2a-2b$

$\large{\boxed{\bf{ \star\:\: a^2+b^2+2a-2b\:\: \star}}}$

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