Question

simplify the following : 1. (a²+a+4)(a-2) , 2. (x-1)(x-2)(x-3) , 3. (x+y)(x-y)(x²+y²)​

Answer 1

1. First step we write the given data

$( {a}^{2} + a + 4)(a - 2)$

$= ( {a}^{2} + a + { {2}^{2} )}(a - 2) \\ = {a}^{3 } - {2}^{3 }$

$= {a}^{3 } - 8$

2. First we write the given data

(x-1)(x-2)(x-3)

We know that

$(x + a)(x + b)(x + c) = {x}^{3} + (a + b + c) {x}^{2} + (ab + bc + ca)x + abc$

$(x - 1)(x - 2)(x - 3) = {x}^{3} + ( - 1 - 2 - 3) {x}^{2} + ( 2 + 6 + 3) {x} + ( - 1 \times - 2 \times - 3)$

$(x - 1)(x - 2)(x - 3) = {x}^{3} - 6 {x}^{2} + 11x - 6$

3. Given:

$(x + y)(x - y)( {x}^{2} + {y}^{2} )$

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

$= ( {x}^{4} - {y}^{4)}$