Question

What is the product?
(X^4)(3x^2-2)(4x^2+5x)

Answer 1

`12x^8+15x^7-8x^6-10x^5`

Explanation:

Start by using the FOIL method on your second and third terms.

`(3x^2-2)(4x^2+5x)\\12x^4+15x^3-8x^2-10x`

Next, multiply the first term (
`x^4`) against your result.

`x^4(12x^4+15x^3-8x^2-10x)\\12x^8+15x^7-8x^6-10x^5`

Answer 2

For this case we must find the product of the following expression:
`(x ^ 4) (3x ^ 2-2) (4x ^ 2 5x) =`

We must bear in mind that to multiply powers of the same base, the same base is placed and the exponents are added:

Multiplying the terms of the first two parentheses, applying distributive property we have:

`(x ^ 4 * 3x ^ 2-x ^ 4 * 2) (4x ^ 2 5x) =\\(3x ^ 6-2x ^ 4) (4x ^ 2 5x) =\\3x ^ 6 * 4x ^ 2 3x ^ 6 * 5x-2x ^ 4 * 4x ^ 2-2x ^ 4 * 5x =\\12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5`

Answer:

The product is:
`12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5`