91Ó°ÊÓ

Every division equation has a related multiplication equation. For instance, \(\frac{16}{2}=8\) means that \(16=2 \cdot 8 .\) What is the related multiplication equation for \(\frac{15 x^{2}+12 x}{3 x}=5 x+4 ?\)

Explain how to rewrite a variable that has a negative exponent as an expression with a positive exponent.

Determine whether the statement is always true, sometimes true, or never true. To multiply a monomial times a polynomial, use the Distributive Property to multiply each term of the polynomial by the monomial.

Determine whether the statement is always true, sometimes true, or never true. The FOIL method is used to multiply two polynomials.

Determine whether the statement is always true, sometimes true, or never true. The product of two binomials is a trinomial.

Is the Distributive Property used to simplify the product \(2(3 x) ?\) If not, what property is used to simplify this expression?

Multiply. $$-y^{4}\left(2 y^{2}-y^{6}\right)$$

For Exercises 7 to \(30,\) divide. $$\frac{8 y^{2}+2 y-3}{y}$$

\(4 x+1\) is a factor of \(4 x^{3}+9 x^{2}-10 x-3 .\) The product of \(4 x+1\) and what polynomial is \(4 x^{3}+9 x^{2}-10 x-3 ?\)

Simplify. $$4 y^{2} z^{4}-\left(2 y z^{2}\right)^{2}$$