Answer
$$(x-(a+bc))(x-(a-bc))=-b^2c^2+a^2-2ax+x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-(a+bc))(x-(a-bc))& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-a-bc)(x-a+bc) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-b^2c^2+a^2-2ax+x^2\end{aligned} $$ | |
| ① | Remove the parentheses by changing the sign of each term within them. $$ - \left( a+bc \right) = -a-bc $$Remove the parentheses by changing the sign of each term within them. $$ - \left( a-bc \right) = -a+bc $$ |
| ② | Multiply each term of $ \left( \color{blue}{x-a-bc}\right) $ by each term in $ \left( x-a+bc\right) $. $$ \left( \color{blue}{x-a-bc}\right) \cdot \left( x-a+bc\right) = \\ = x^2-ax+ \cancel{bcx}-ax+a^2 -\cancel{abc} -\cancel{bcx}+ \cancel{abc}-b^2c^2 $$ |
| ③ | Combine like terms: $$ x^2 \color{blue}{-ax} + \, \color{red}{ \cancel{bcx}} \, \color{blue}{-ax} +a^2 \, \color{orange}{ -\cancel{abc}} \, \, \color{red}{ -\cancel{bcx}} \,+ \, \color{orange}{ \cancel{abc}} \,-b^2c^2 = -b^2c^2+a^2 \color{blue}{-2ax} +x^2 $$ |
This page was created using
Simplify polynomials calculator