91Ó°ÊÓ

Give an example of each. a. a difference of two squares b. a square of a difference c. a sum of two squares d. a sum of two cubes e. a cube of a sum

Terms having the same variables with the same exponents are _____ called

a. Explain why the number \(60.22 \times 10^{22}\) is not written in scientific notation. b. Explain why the number \(0.6022 \times 10^{24}\) is not written in scientific notation.

Fill in the blanks. The product of the sum and difference of the same two terms is the \(\quad\) of the first term minus the \(\quad\) of the second term. $$ (x+y)(x-y)= $$

Fill in the blanks. If a polynomial has three terms, try to factor it as a ________.

The prime factorizations of three terms are shown. Find their GCF. $$ \begin{array}{l} 12 x^{2} y^{3}=2 \cdot 2 \cdot 3 \cdot x \cdot x \cdot y \cdot y \cdot y \\ 18 x y^{4}=2 \cdot 3 \cdot 3 \cdot x \cdot y \cdot y \cdot y \cdot y \\ 126 x^{3} y^{2}=2 \cdot 3 \cdot 3 \cdot 7 \cdot x \cdot x \cdot x \cdot y \cdot y \end{array} $$

Fill in the blanks. $$ \text { a. } 36 y^{2}-49 m^{4}=(\quad)^{2}-(\quad)^{2} $$ $$ \text { b. } 125 h^{3}-27 k^{6}=(\quad)^{3}-(\quad)^{3} $$

Fill in the blanks. If a polynomial has four or more terms, try factoring it by ________.

Complete the rules for exponents. Assume that there are no divisions by \(0 .\) a. To multiply exponential expressions with the same base, such as \(x^{3} \cdot x^{8},\) keep the common base \(x\) and _________ the exponents. b. To divide exponential expressions with the same base, such as \(\frac{a^{\prime}}{a^{4}},\) keep the common base \(a\) and _______ the exponents.

Fill in the blanks to complete each factorization. a. \(8 x^{3}+6 x^{2}+2 x=2 x\left(4 x^{2}+3 x+ \quad\right)\) b. \(-9 x+5=-(9 x \quad-5)\)