Question
Answer
$$x^6-8x^5+24x^4-33x^3+20x^2-4x-(x^5-8x^4+22x^3-25x^2+10x)=x^6-9x^5+32x^4-55x^3+45x^2-14x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x^6-8x^5+24x^4-33x^3+20x^2-4x-(x^5-8x^4+22x^3-25x^2+10x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^6-8x^5+24x^4-33x^3+20x^2-4x-x^5+8x^4-22x^3+25x^2-10x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^6-9x^5+32x^4-55x^3+45x^2-14x\end{aligned} $$ | |
| ① | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^5-8x^4+22x^3-25x^2+10x \right) = -x^5+8x^4-22x^3+25x^2-10x $$ |
| ② | Combine like terms: $$ x^6 \color{blue}{-8x^5} + \color{red}{24x^4} \color{green}{-33x^3} + \color{orange}{20x^2} \color{blue}{-4x} \color{blue}{-x^5} + \color{red}{8x^4} \color{green}{-22x^3} + \color{orange}{25x^2} \color{blue}{-10x} = \\ = x^6 \color{blue}{-9x^5} + \color{red}{32x^4} \color{green}{-55x^3} + \color{orange}{45x^2} \color{blue}{-14x} $$ |
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