Question

(4x-7)(3x-1)-(3x-5)(5x-1)

Answer 1

`(4x-7)(3x-1)-(3x-5)(5x-1)=-3x^2+3x+2.`

Explanation:

Calculate the expressions in brackets separately:

1.
`(4x-7)(3x-1)=4x\cdot 3x+4x\cdot (-1)+(-7)\cdot 3x+(-7)\cdot (-1)=12x^2-4x-21x+7=12x^2-25x+7.`

2.
`(3x-5)(5x-1)=3x\cdot 5x+3x\cdot (-1)+(-5)\cdot 5x+(-5)\cdot (-1)=15x^2-3x-25x+5=15x^2-28x+5.`

Then

`(4x-7)(3x-1)-(3x-5)(5x-1)=(12x^2-25x+7)-(15x^2-28x+5)=12x^2-25x+7-15x^2+28x-5=-3x^2+3x+2.`