Answer Key 6.5
[latexpage]
- \(6p-42\)
- \(32k^2+16k\)
- \(12x+6\)
- \(18n^3+21n^2\)
- \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&8n&+&8&& \\
\times &4n&+&6&& \\
\midrule
&32n^2&+&32n&& \\
&&&48n&+&48 \\
\midrule
&32n^2&+&80n&+&48
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&x&-&4&& \\
\times &2x&+&1&& \\
\midrule
&2x^2&-&8x&& \\
&&&x&-&4 \\
\midrule
&2x^2&-&7x&-&4
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&7b&-&5&& \\
\times &8b&+&3&& \\
\midrule
&56b^2&-&40b&& \\
&&+&21b&-&15 \\
\midrule
&56b^2&-&19b&-&15
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&4r&+&8&& \\
\times &r&+&8&& \\
\midrule
&4r^2&+&8r&& \\
&&+&32r&+&64 \\
\midrule
&4r^2&+&40r&+&64
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&5v&-&2&& \\
\times &3v&-&4&& \\
\midrule
&15v^2&-&6v&& \\
&&-&20v&+&8 \\
\midrule
&15v^2&-&26v&+&8
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&a&-&8&& \\
\times &6a&+&4&& \\
\midrule
&6a^2&-&48a&& \\
&&+&4a&-&32 \\
\midrule
&6a^2&-&44a&-&32
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&6x&-&4y&& \\
\times &5x&+&y&& \\
\midrule
&30x^2&-&20xy&& \\
&&+&6xy&-&4y^2 \\
\midrule
&30x^2&-&14xy&-&4y^2
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&8u&-&7v&& \\
\times &2u&+&3v&& \\
\midrule
&16u^2&-&14uv&& \\
&&+&24uv&-&21v^2 \\
\midrule
&16u^2&+&10uv&-&21v^2
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&8x&+&3y&& \\
\times &7x&+&5y&& \\
\midrule
&56x^2&+&21xy&& \\
&&+&40xy&+&15y^2 \\
\midrule
&56x^2&+&61xy&+&15y^2
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\
&a&-&3b&& \\
\times &5a&+&8b&& \\
\midrule
&5a^2&-&15ab&& \\
&&+&8ab&-&24b^2 \\
\midrule
&5a^2&-&7ab&-&24b^2
\end{array}\) - \(\begin{array}{rrrrrrrr}
\\ \\ \\ \\ \\
&6r^2&-&r&+&5&& \\
\times &&&r&-&7&& \\
\midrule
&6r^3&-&r^2&+&5r&& \\
&&-&42r^2&+&7r&-&35 \\
\midrule
&6r^3&-&43r^2&+&12r&-&35
\end{array}\) - \(\begin{array}{rrrrrrrr}
\\ \\ \\ \\ \\
&4x^2&+&3x&+&5&& \\
\times &&&4x&+&8&& \\
\midrule
&16x^3&+&12x^2&+&20x&& \\
&&+&32x^2&+&24x&+&40 \\
\midrule
&16x^3&+&44x^2&+&44x&+&40
\end{array}\) - \(\begin{array}{rrrrrrrr}
\\ \\ \\ \\ \\
&2n^2&-&2n&+&5&& \\
\times &&&6n&-&4&& \\
\midrule
&12n^3&-&12n^2&+&30n&& \\
&&-&8n^2&+&8n&-&20 \\
\midrule
&12n^3&-&20n^2&+&38n&-&20
\end{array}\) - \(\begin{array}{rrrrrrrr}
\\ \\ \\ \\ \\
&4b^2&+&4b&+&4&& \\
\times &&&2b&-&3&& \\
\midrule
&8b^3&+&8b^2&+&8b&& \\
&&-&12b^2&-&12b&-&12 \\
\midrule
&8b^3&-&4b^2&-&4b&-&12
\end{array}\) - \(\begin{array}{rrrrrrrr}
\\ \\ \\ \\ \\
&6x^2&-&7xy&+&4y^2&& \\
\times &&&6x&+&3y&& \\
\midrule
&36x^3&-&42x^2y&+&24xy^2&& \\
&&+&18x^2y&-&21xy^2&+&12y^3 \\
\midrule
&36x^3&-&24x^2y&+&3xy^2&+&12y^3
\end{array}\) - \(\begin{array}{rrrrrrrr}
\\ \\ \\ \\ \\
&7m^2&+&6mn&+&4n^2&& \\
\times &&&3m&-&2n&& \\
\midrule
&21m^3&+&18m^2n&+&12mn^2&& \\
&&-&14m^2n&-&12mn^2&-&8n^3 \\
\midrule
&21m^3&+&4m^2n&-&8n^3&&
\end{array}\) - \(\begin{array}{rrrrrrrrrr}
\\ \\ \\ \\ \\ \\
&6n^2&-&5n&+&6&&&& \\
\times&8n^2&+&4n&+&6&&&& \\
\midrule
&48n^4&-&40n^3&+&48n^2&&&& \\
&&+&24n^3&-&20n^2&+&24n&& \\
&&&&+&36n^2&-&30n&+&36 \\
\midrule
&48n^4&-&16n^3&+&64n^2&-&6n&+&36
\end{array}\) - \(\begin{array}{rrrrrrrrrr}
\\ \\ \\ \\ \\ \\
&7a^2&-&6a&+&1&&&& \\
\times&2a^2&+&6a&+&3&&&& \\
\midrule
&14a^4&-&12a^3&+&2a^2&&&& \\
&&+&42a^3&-&36a^2&+&6a&& \\
&&&&+&21a^2&-&18a&+&3 \\
\midrule
&14a^4&+&30a^3&-&13a^2&-&12a&+&3
\end{array}\) - \(\begin{array}{rrrrrrrrrr}
\\ \\ \\ \\ \\ \\
&3k^2&+&3k&+&6&&&& \\
\times&5k^2&+&3k&+&3&&&& \\
\midrule
&15k^4&+&15k^3&+&30k^2&&&& \\
&&+&9k^3&+&9k^2&+&18k&& \\
&&&&+&9k^2&+&9k&+&18 \\
\midrule
&15k^4&+&24k^3&+&48k^2&+&27k&+&18
\end{array}\) - \(\begin{array}{rrrrrrrrrr}
\\ \\ \\ \\ \\ \\
&6u^2&+&4uv&+&3v^2&&&& \\
\times &7u^2&+&8uv&-&6v^2&&&& \\
\midrule
&42u^4&+&28u^3v&+&21u^2v^2&&&& \\
&&+&48u^3v&+&32u^2v^2&+&24uv^3&& \\
&&&&-&36u^2v^2&-&24uv^3&-&18v^4 \\
\midrule
&42u^4&+&76u^3v&+&17u^2v^2&-&18v^4&& \\
\end{array}\) - \(\begin{array}{rrrrrrrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\
&2n^3&-&8n^2&+&3n&+&6&&&&&& \\
\times&n^3&-&6n^2&-&2n&+&3&&&&&& \\
\midrule
&2n^6&-&8n^5&+&3n^4&+&6n^3&&&&&& \\
&&-&12n^5&+&48n^4&-&18n^3&-&36n^2&&&& \\
&&&&-&4n^4&+&16n^3&-&6n^2&-&12n&& \\
&&&&&&+&6n^3&-&24n^2&+&9n&+&18 \\
\midrule
&2n^6&-&20n^5&+&47n^4&+&10n^3&-&66n^2&-&3n&+&18
\end{array}\) - \(\begin{array}{rrrrrrrrrrrrrr}
\\ \\ \\ \\ \\ \\ \\
&a^3&+&2a^2&+&3a&+&3&&&&&& \\
\times&a^3&+&2a^2&-&4a&+&1&&&&&& \\
\midrule
&a^6&+&2a^5&+&3a^4&+&3a^3&&&&&& \\
&&+&2a^5&+&4a^4&+&6a^3&+&6a^2&&&& \\
&&&&-&4a^4&-&8a^3&-&12a^2&-&12a&& \\
&&&&&&+&a^3&+&2a^2&+&3a&+&3 \\
\midrule
&a^6&+&4a^5&+&3a^4&+&2a^3&-&4a^2&-&9a&+&3
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\ \\
&2x&+&1&& \\
\times &3x&-&4&& \\
\midrule
&6x^2&+&3x&& \\
&&-&8x&-&4 \\
\midrule
&3(6x^2&-&5x&-&4) \\
&18x^2&-&15x&-&12
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\ \\
&2x&-&3&& \\
\times &x&-&4&& \\
\midrule
&2x^2&-&3x&& \\
&&-&8x&+&12 \\
\midrule
&5(2x^2&-&11x&+&12) \\
&10x^2&-&55x&+&60
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\ \\
&4x&-&5&& \\
\times &2x&+&1&& \\
\midrule
&8x^2&-&10x&& \\
&&+&4x&-&5 \\
\midrule
&3(8x^2&-&6x&-&5) \\
&24x^2&-&18x&-&15
\end{array}\) - \(\begin{array}{rrrrrr}
\\ \\ \\ \\ \\ \\
&2x&-&6&& \\
\times &4x&+&1&& \\
\midrule
&8x^2&-&24x&& \\
&&+&2x&-&6 \\
\midrule
&2(8x^2&-&22x&-&6) \\
&16x^2&-&44x&-&12
\end{array}\)
