Question

simplyfy (a+1)(a-1)(a2-1)​

Answer 1

Question:→

Simplify (a+1)(a-1)(a²-1)

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$\mathtt{ (a+1)(a-1)(a²-1)}$

$\mathtt{ = (a+1)(a-1)(a-1)(a + 1)}$

$\mathtt{ = {(a + 1)}^{2} \times {(a - 1)}^{2} }$

$\mathtt{ = ((a + 1)(a -1 ))^{2} }$

$\mathtt{ = ({a}^{2} - 1)^{2} }$

$\mathtt{ \color{red}{ \boxed{ \bold{ = {a}^{4} - 2 {a}^{2} + 1}}}}$

Formula used :—

${ \mathtt{ \boxed{ \bold{(x + y)(x - y) = {x}^{2} - {y}^{2} }}}}$

${ \mathtt{ \boxed{ \bold{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }}}}$

${ \mathtt{ \boxed{ \bold{ {x}^{m} \: \times {y}^{m} = (x.y)^{m} }}}}$