91Ó°ÊÓ

Multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. $$ (2 x+3 y)^{2} $$

In Problems 87-96, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not \(0 .\) \(\left(9 x^{4}\right)^{2}\)

Simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not \(0 .\) \(\left(-4 x^{2}\right)^{-1}\)

Use the Distributive Property to remove the parentheses. $$ 6(x+4) $$

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime. $$ x^{2}+4 x+16 $$

Simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not \(0 .\) \(\left(x^{-1} y\right)^{3}\)

Simplify each expression. $$\left(-\frac{64}{125}\right)^{-2 / 3}$$

Find the quotient and the remainder. Check your work by verifying that Quotient \(\cdot\) Divisor \(+\) Remainder \(=\) Dividend $$ 3 x^{3}-x^{2}+x-2 \text { divided by } x+2 $$

Simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not \(0 .\) \(\left(\frac{2 x^{-3}}{3 y^{-1}}\right)^{-2}\)

An electrical circuit contains three resistors connected in parallel. If these three resistors provide resistance of \(R_{1}, R_{2},\) and \(R_{3}\) ohms, respectively, their combined resistance \(R\) is given by the formula $$ \frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} $$ Express \(R\) as a rational expression. Evaluate \(R\) for \(R_{1}=5\) ohms, \(R_{2}=4\) ohms, and \(R_{3}=10\) ohms.