Question

Choose the correct simplification of the expression −5x2(4x − 6x2 − 3).

30x4 − 20x3 + 15x2
−11x4 − x3 − 8x2
−30x4 + 20x3 − 15x2
30x4 + 20x3 + 15x2

Answer 1

Option A is correct

`30x^4-20x^3+15x^2`

Explanation:

The distributive property says that:

`a \cdot (x +y +z) = a\cdot x+ a\cdot y+ a\cdot z`

Given the expression:
`5x^2(4x-6x^2-3)`

Using distributive property :

`-5x^2 \cdot (4x) - 5x^2 \cdot (-6x^2) -5x^2 \cdot (-3)`

Use:
`x^a \cdot x^b = x^(a+b)`

then;

`-20x^3+30x^4+15x^2`

or

`30x^4-20x^3+15x^2`

Therefore, the correct simplification of the given expression is
`30x^4-20x^3+15x^2`

Answer 2

If you would like to solve -5x^2 * (4x - 6x^2 - 3), you can do this using the following steps:

-5x^2 * (4x - 6x^2 - 3) = (-5x^2) * 4x - (-5x^2) * 6x^2 - (-5x^2) * 3 = -20x^3 + 30x^4 + 15x^2 = 30x^4 - 20x^3 + 15x^2

The correct result would be 30x^4 - 20x^3 + 15x^2.