Find the product. (25x 2 + 20xy + 16y 2)(5x - 4y)

Hello! And thank you for your question!

First Distribute:

25x​^2​​(5x−4y)+20xy(5x−4y)+16y​^2​​(5x−4y)

Then distribute again:

125x​^3​​−100x​^2​​y+20xy(5x−4y)+16y​^2​​(5x−4y)

Distrubute another time:

125x​^3​​−100x​^2​​y+100x​^2​​y−80xy​^2​​+16y​^2​​(5x−4y)

And one last time distrubute:

125x​^3​​−100x​^2​​y+100x^2​​y−80xy​^2​​+80y​^2​​x−64y​3​​

After distributing Simplify:

125x​^3​​−80xy​^2​​+80y​^2​​x−64y​3​​

Combine like terms:

125x​^3​​+(−80xy​^2​​+80xy​^2​​)−64y​3​​

Lastly simplify once more:

125x^3 - 64y^2

Final

125x^3 - 64y^2