simplify <br/>10(x−1)2+5(x−1)10\left(x-1\right)^2+5\left(x-1\right)

asked by guest
on Jan 20, 2025 at 2:14 pm



You asked:

Simplify the expression: 10(x−1)2+5(x−1)10 {\left( x - 1 \right)}^{2} + 5 \left(x - 1\right)

MathBot Answer:

Simplified:

10(x−1)2+5(x−1)=5x+10(x−1)2−5 10 {\left( x - 1 \right)}^{2} + 5 \left(x - 1\right) = 5 x + 10 \left(x - 1\right)^{2} - 5

10(x−1)2+5(x−1)=10(x2−2x+1)+5(x−1)=10(x2−2x+1)+5x−5=10x2−20x+10+5x−5=10x2−15x+5\begin{aligned}10 \left(x - 1\right)^{2} + 5 \left(x - 1\right)&=10 \left(x^{2} - 2 x + 1\right) + 5 \left(x - 1\right)\\&=10 \left(x^{2} - 2 x + 1\right) + 5 x - 5\\&=10 x^{2} - 20 x + 10 + 5 x - 5\\&=10 x^{2} - 15 x + 5\end{aligned}

Expanded:

10(x−1)2+5(x−1)=10x2−15x+5 10 {\left( x - 1 \right)}^{2} + 5 \left(x - 1\right) = 10 x^{2} - 15 x + 5

Factored:

10(x−1)2+5(x−1)=5⋅(2x−1)(x−1) 10 {\left( x - 1 \right)}^{2} + 5 \left(x - 1\right) = 5 \cdot \left(2 x - 1\right) \left(x - 1\right)


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