Answer
$$10x^2+6x-1-(x+3)(x+3)=9x^2-10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10x^2+6x-1-(x+3)(x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10x^2+6x-1-(x^2+3x+3x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10x^2+6x-1-(x^2+6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10x^2+6x-1-x^2-6x-9 \xlongequal{ } \\[1 em] & \xlongequal{ }10x^2+ \cancel{6x}-1-x^2 -\cancel{6x}-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9x^2-10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+3}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x+3}\right) \cdot \left( x+3\right) = x^2+3x+3x+9 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} + \color{blue}{3x} +9 = x^2+ \color{blue}{6x} +9 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2+6x+9 \right) = -x^2-6x-9 $$ |
| ④ | Combine like terms: $$ \color{blue}{10x^2} + \, \color{red}{ \cancel{6x}} \, \color{orange}{-1} \color{blue}{-x^2} \, \color{red}{ -\cancel{6x}} \, \color{orange}{-9} = \color{blue}{9x^2} \color{orange}{-10} $$ |
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