Question

Select all the statements that are true.

Question 4 options:

The product of 8x(5x−6) is 40x^2−48x


The product of −4x(2x2+1) is −8x^3−5x

The product of (x−3)(5x−6) is 5x^2−21x+18

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

Answer 1

The product of 8x(5x−6) is 40x^2−48x

The product of (x−3)(5x−6) is 5x^2−21x+18

Explanation:

Verify each option

Part 1) The product of 8x(5x−6) is 40x^2−48x

we have

`8x(5x-6)`

Applying distributive property

`8x(5x)-8x(6)\\40x^2-48x`

Compare with the given value

`40x^2-48x=40x^2-48x`

therefore

The statement is true

Part 2) The product of −4x(2x2+1) is −8x^3−5x

we have

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

Applying distributive property

`-4x(2x^(2))-4x(1)\\-8x^3-4x`

Compare with the given value

`-8x^3-4x \\eq -8x^3-5x`

therefore

The statement is not true

Part 3) The product of (x−3)(5x−6) is 5x^2−21x+18

we have

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

Applying distributive property

`x(5x)-x(6)-3(5x)+3(6)\\5x^2-6x-15x+18\\5x^2-21x+18`

Compare with the given value

`5x^2-21x+18=5x^2-21x+18`

therefore

The statement is true

Part 4) The product of (2x+3)(x^2+3x−5) is 2x^3+9x^2+9x−25

we have

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

Applying distributive property

`(2x)(x^2+3x-5)+(3)(x^2+3x-5)\\(2x^3+6x^2-10x)+(3x^2+9x-15)\\2x^3+9x^2-x-15`

Compare with the given value

`2x^3+9x^2-x-15 \\eq 2x^3+9x^2+9x-25`

therefore

The statement is not true