Question
Answer
$$(x+5)(x-5)-(x+2)(x+8)=-10x-41$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+5)(x-5)-(x+2)(x+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-5x+5x-25-(x^2+8x+2x+16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-25-(x^2+10x+16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2-25-x^2-10x-16 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{x^2}-25 -\cancel{x^2}-10x-16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-10x-41\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+5}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x+5}\right) \cdot \left( x-5\right) = x^2 -\cancel{5x}+ \cancel{5x}-25 $$Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x+8\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x+8\right) = x^2+8x+2x+16 $$ |
| ② | Combine like terms: $$ x^2 \, \color{blue}{ -\cancel{5x}} \,+ \, \color{blue}{ \cancel{5x}} \,-25 = x^2-25 $$Combine like terms: $$ x^2+ \color{blue}{8x} + \color{blue}{2x} +16 = x^2+ \color{blue}{10x} +16 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2+10x+16 \right) = -x^2-10x-16 $$ |
| ④ | Combine like terms: $$ \, \color{blue}{ \cancel{x^2}} \, \color{green}{-25} \, \color{blue}{ -\cancel{x^2}} \,-10x \color{green}{-16} = -10x \color{green}{-41} $$ |
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