Question

1. \\((2r + 2s)^2\\)
2. \\((u^2 + u^3)(u^3 - u^2 + u - 1)\\)

divide the polynomials.

1. \\((-80w^6 + 35w^5 - 50w^4) \div 10w^4\\)
2. \\((24y^3 - 2y^2) \div 2y\\)

Explanation:

Expand the perfect square trinomial

Using the Perfect Square Trinomials knowledge point

$$ (2r + 2s)^2 = (2r)^2 + 2(2r)(2s) + (2s)^2 $$

$$ = 4r^2 + 8rs + 4s^2 $$

Multiply the polynomials

Using the Polynomial Multiplication knowledge point

$$ (u^2 + u^3)(u^3 - u^2 + u - 1) = u^2(u^3 - u^2 + u - 1) + u^3(u^3 - u^2 + u - 1) $$

$$ = (u^5 - u^4 + u^3 - u^2) + (u^6 - u^5 + u^4 - u^3) $$

$$ = u^6 + (u^5 - u^5) + (-u^4 + u^4) + (u^3 - u^3) - u^2 $$

$$ = u^6 - u^2 $$

Divide the first polynomial by the monomial

Using the Polynomial Division and Monomial Division knowledge points

$$ (-80w^6 + 35w^5 - 50w^4) \div 10w^4 = \frac{-80w^6}{10w^4} + \frac{35w^5}{10w^4} - \frac{50w^4}{10w^4} $$

$$ = -8w^2 + \frac{7}{2}w - 5 $$

Divide the second polynomial by the monomial

Using the Polynomial Division and Monomial Division knowledge points

$$ (24y^3 - 2y^2) \div 2y = \frac{24y^3}{2y} - \frac{2y^2}{2y} $$

$$ = 12y^2 - y $$

Answer:

Question 28

\(4r^2 + 8rs + 4s^2\)

Question 30

\(u^6 - u^2\)

Question 32

\(-8w^2 + \frac{7}{2}w - 5\)

Question 34

\(12y^2 - y\)