Question

a)(x+3)(x-2)+(x-3)^2

b)(x+2)^2+(x+1)(x-1)

c)(2x-5)(1-x)-(x-3)(-2x)

d)(x-2)(x-1)(x+3)-x^2(x-5)

e)(4x+3)(x^2+7x-2)

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Answer 1

`(x+3)(x-2)+(x-3)^2`

`=x^2+x -6+x^2 -6x+9`

`=(x^2+x^2)+(x-6x) + (-6+9)`

`=2x^2 - 5x + 3`

_______________________________

`(x+2)^2+(x+1)(x-1)`

`=x^2 + 4x +4 + x^2-1`

`=2x^2 +4x+3`

______________________________

`(2x-5)(1-x)-(x-3)(-2x)`

`=-2x^2 +7x-5 +2x^2 -6x`

`= x - 5`

____________________________

`(x-2)(x-1)(x+3)-x^2(x-5)`

`=x^3 -7x+6-x^3 +5x^2`

`=5x^2 -2x +6`

_____________________________

`(4x+3)(x^2+7x-2)`

`=4x^3 +31x^2 +13x-6`

 

Answer 2

`(a):(x+3)(x-2)+(x-3)^{2}=x^{2}+3x-2x-6+x^{2}-6x+9`

`=2x^{2}-5x+3`

`(b):(x+2)^{2}+(x+1)(x-1)=x^{2}+4x+4+x^{2}-1`

`=2x^{2}+4x+3`

`(c):(2x-5)(1-x)-(x-3)(-2x)=2x-5-2x^{2}+5x+2x^{2}-6x`

`=x-5`

`(d):(x-2)(x-1)(x+3)-x^{2}(x-5)=(x^{2}-3x+2)(x+3)-x^{3}+5x^{2}`

`=x^{3}-3x^{2}+2x+3x^{2}-9x+6-x^{3}+5x^{2}`

`=5x^{2}-4x+6`

`(e):(4x+3)(x^{2}+7x-2)=4x^{3}+28x^{2}-8x+3x^{2}+21x-6`

`=4x^{3}+31x^{2}+13x-6`

Answer 3

( a ) : ( x + 3 ) ( x − 2 ) + ( x − 3 ) 2 = x 2 + 3 x − 2 x − 6 + x 2 − 6 x + 9 = 2 x 2 − 5 x + 3 ( b ) : ( x + 2 ) 2 + ( x + 1 ) ( x − 1 ) = x 2 + 4 x + 4 + x 2 − 1 = 2 x 2 + 4 x + 3 ( c ) : ( 2 x − 5 ) ( 1 − x ) − ( x − 3 ) ( − 2 x ) = 2 x − 5 − 2 x 2 + 5 x + 2 x 2 − 6 x = x − 5 ( d ) : ( x − 2 ) ( x − 1 ) ( x + 3 ) − x 2 ( x − 5 ) = ( x 2 − 3 x + 2 ) ( x + 3 ) − x 3 + 5 x 2 = x 3 − 3 x 2 + 2 x + 3 x 2 − 9 x + 6 − x 3 + 5 x 2 = 5 x 2 − 4 x + 6 ( e ) : ( 4 x + 3 ) ( x 2 + 7 x − 2 ) = 4 x 3 + 28 x 2 − 8 x + 3 x 2 + 21 x − 6

Answer 4

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