91Ó°ÊÓ

Find each product. As we said in the Section 5.3 opener, cut to the chase in each part of the polynomial multiplication: Use only the special-product formula for the sum and difference of two terms or the formulas for the square of a binomial. $$\left[\left(x^{3} y^{3}+1\right)\left(x^{3} y^{3}-1\right)\right]^{2}$$

use a vertical format to subtract the polynomials. $$\begin{array}{r} 7 x^{3}+5 x^{2}-3 \\ -\left(-2 x^{3}-6 x^{2}+5\right) \\ \hline \end{array}$$

Simplify each expression. $$\left(\frac{18 x^{2} y^{4}}{9 x y^{2}}\right)-\left(\frac{15 x^{5} y^{6}}{5 x^{4} y^{4}}\right)$$

Multiply using the method of your choice. $$\left(\frac{1}{4} x^{2}+12\right)\left(\frac{3}{4} x^{2}-8\right)$$

In Exercises \(79-90\), write each number in decimal notation without the use of exponents. $$9.23 \times 10^{5}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Each statement applies to the division problem $$\frac{x^{3}+1}{x+1}$$ Rewriting \(x^{3}+1\) as \(x^{3}+0 x^{2}+0 x+1\) can change the value of the variable expression for certain values of \(x .\)

Use a vertical format to find each product. $$\begin{array}{r} x^{2}-3 x+9 \\ 2 x-3 \\ \hline \end{array}$$

Find each product. As we said in the Section 5.3 opener, cut to the chase in each part of the polynomial multiplication: Use only the special-product formula for the sum and difference of two terms or the formulas for the square of a binomial. $$\left[\left(1-a^{3} b^{3}\right)\left(1+a^{3} b^{3}\right)\right]^{2}$$

Use a vertical format to find each product. $$\begin{array}{r} y^{2}-5 y+3 \\ 4 y-5 \\ \hline \end{array}$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Each statement applies to the division problem $$\frac{x^{3}+1}{x+1}$$ There's no need to apply the long-division process to this problem because I can work the problem in my head and see that the quotient must be \(x^{2}+1\)