(5x2 -4x)(3x2+2x)

*** it is supposed to be 5x(to the power of two) and 3x(to the power of two)

Just expand it using FOIL

Your first line will have 4 terms, you can add up the two middle terms.

(5x^2 - 4x)(3x^2 + 2x)

Use FOIL to expand
-8x^2 - 2x^3 + 15x^4
15x^4 - 2x^3 - 8x^2

9x^2-4x+3

This is already fully expanded and cannot be simplified further.

To multiply the expressions (5x2 - 4x) and (3x2 + 2x), we will use the distributive property, which states that a(b + c) = ab + ac.

First, let's distribute 5x2 to both terms in the second expression:

5x2 * 3x2 = (5 * 3) * (x2 * x2) = 15x4

5x2 * 2x = (5 * 2) * (x2 * x) = 10x3

Similarly, let's distribute -4x to both terms in the second expression:

-4x * 3x2 = (-4 * 3) * (x * x2) = -12x3

-4x * 2x = (-4 * 2) * (x * x) = -8x2

Now, we can combine the like terms by adding or subtracting them:

15x4 + 10x3 - 12x3 - 8x2

Combining the like terms:

15x4 + (10x3 - 12x3) - 8x2 = 15x4 - 2x3 - 8x2

So, the product of (5x2 - 4x) and (3x2 + 2x) is 15x4 - 2x3 - 8x2.