Question

What is the product? (3x-6) (2x^2 -7x+1)

Answer 1

(3x - 6)(2x² - 7x + 1)
3x(2x² - 7x + 1) - 6(2x² - 7x + 1)
3x(2x²) - 3x(7x) + 3x(1) - 6(2x²) + 6(7x) - 6(1)
6x³ - 21x² + 3x - 12x² + 42x - 6
6x³ - 21x² - 12x² + 3x + 42x - 6
6x³ - 33x² + 45x - 6

Answer 2

`\left(3x-6\right)\left(2x^2-7x+1\right)=6x^3-33x^2+45x-6`

Solution-

Given the two polynomials are
`3x-6, 2x^2 -7x+1`

So their product will be,

`=\left(3x-6\right)\left(2x^2-7x+1\right)`

Distributing the Parentheses,

`=3x\cdot \:2x^2+3x\left(-7x\right)+3x\cdot \:1+\left(-6\right)\cdot \:2x^2+\left(-6\right)\left(-7x\right)+\left(-6\right)\cdot \:1`

Applying minus-plus rules,

`=3\cdot \:2x^2x-3\cdot \:7xx+3\cdot \:1\cdot \:x-6\cdot \:2x^2+6\cdot \:7x-6\cdot \:1`

Simplifying further,

`=6x^3-33x^2+45x-6`