Question

expand the following a)(x-y)2 b) (a-b)3 c)(a+b)3 d)x3+y3 e) (x+y)(x-y)​

Answer 1

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Question :Expand the following :

(a) (x-y)²

(b) (a-b)³

(c) (a+b)³

(d) x³+y³

(e) (x+y)(x-y)

$\: \bigstar \large \bold \pink{ \underline{answer}}$

$\star \bf{(1) {(x - y)}^{2} }$

$\implies \sf{ {x}^{2} + {y}^{2} - 2xy}$

$\star \bf{(2) \: ( {a - b)}^{3} }$

$\: \implies \bf{(a - b)( {a}^{2} + ab + {b}^{2} )}$

$\star \bf{(3) \: ( {a + b)}^{3} }$

$\: \implies \sf{ (a + b)( {a}^{2} + ab + {b}^{2} )} \: \: or$

$\: \: \implies \sf{ {a}^{3} + {b}^{3} + 3 {a}^{2} b + 3 {b}^{2} a}$

$\: \star \bf{(4) \: {x}^{3} + {y}^{3} }$

$\: \\ \implies \sf{ {(x + y)}^{3} } = (x + y)( {x}^{2} + xy + {y}^{2} )$

$\: \star \bf{(5) \: (x + y)(x - y)}$

$\: \implies \sf{(x + y)(x - y)}$

$\: \: \implies \sf{x(x - y) + y(x - y)}$

$\: \implies \sf{ {x}^{2} - xy + yx - {y}^{2} }$

$\: \: \implies \sf{ {x}^{2} - {y}^{2} }$