Question

Select all the statements that are true.

Question 4 options:

The product of 8x(5x−6) is 40x2−48x


The product of −4x(2x2+1) is −8x3−5x

The product of (x−3)(5x−6) is 5x2−21x+18

The product of (2x+3)(x2+3x−5) is 2x3+9x2+9x−25

Answer 1

The product of 8x(5x−6) is 40x2−48x

The product of (x−3)(5x−6) is 5x2−21x+18

Explanation:

Verify each case

case 1) The product of 8x(5x−6) is 40x2−48x

we have

`8x(5x-6)`

Apply distributive property

`8x(5x)-8x(6)`

`40x^2-48x`

Compare

`40x^2-48x=40x^2-48x` ----> is true

case 2) The product of −4x(2x2+1) is −8x3−5x

we have

`-4x(2x^2+1)`

Apply distributive property

`-4x(2x^2)-4x(1)`

`-8x^3-4x`

Compare

`-8x^3-4x=-8x^3-5x` -----> is not true

case 3) The product of (x−3)(5x−6) is 5x2−21x+18

we have

`(x-3)(5x-6)`

Apply distributive property

`x(5x)-x(6)-3(5x)+3(6)`

`5x^2-6x-15x+18`

`5x^2-21x+18`

Compare

`5x^2-21x+18=5x^2-21x+18` ----> is true

case 4) The product of (2x+3)(x2+3x−5) is 2x3+9x2+9x−25

we have

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

Apply distributive property

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

`2x^3+6x^2-10x+3x^2+9x-15`

`2x^3+9x^2+2x-15`

Compare

`2x^3+9x^2+2x-15=2x^3+9x^2+9x-25` ----> is not true