Question

1) 2x. ( x - 5 ) + ( x - 2 ) . ( x + 3 )

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

3 ) ( 4x - 3 ) . ( 4x - 3 ) - ( 3x + 2 ) . ( 3x - 2 )

4 ) ( 2x - 1 ) . ( 2x + 1 ) . ( 2x + 1 ) -4 . ( x² + 1 ) 

5 )  3x . ( 2x - 8 ) - ( 2 - 6x ) . ( 5 + x )

6 ) x . ( 3x - 18 ) - 3 . ( x - 4 ) . ( x - 2 ) + 8

7 ) ( x + 2 ) . ( x² - 2x + 4 ) - x² . ( x - 2 ) - 2x²

 

Answer 1

1) \(2x\left(x-5\right)+\left(x-2\right)\left(x+3\right)=2x^2-10x+x^2+3x-2x-6=3x^2-9x-6\)

2) \(\left(2x-5\right)\left(1-x\right)-\left(x-3\right)\left(-2x\right)=2x-2x^2-5+5x+2x^2-6x=x-5\)

3) \(\left(4x-3\right)\left(4x-3\right)-\left(3x+2\right)\left(3x-2\right)=\left(4x-3\right)^2-9x^2+4=16x^2-24x+9-9x^2+4\)

\(=7x^2-24x+13\)

4) \(\left(2x-1\right)\left(2x+1\right)\left(2x+1\right)-4\left(x^2+1\right)=\left(2x-1\right)[\left(2x+1\right)^2]-4x^2-4\)

\(=\left(2x-1\right)\left(4x^2+4x+4\right)-4x^2-4=8x^3+8x^2+8x-4x^2-4x-4-4x^2-4=8x^3+4x-8\)

Answer 2

5) \(3x\left(2x-8\right)-\left(2-6x\right)\left(5+x\right)=6x^2-24x-10-2x+30x+6x^2=12x^2+4x-10\)

6) \(x\left(3x-18\right)-3\left(x-4\right)\left(x-2\right)+8=3x^2-18x-3x^2+6x+12x-24+8=-16\)

7) \(\left(x+2\right)\left(x^2-2x+4\right)-x^2\left(x-2\right)-2x^2=x^3+8-x^3+2x^2-2x^2=8\)