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

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



You asked:

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

MathBot Answer:

Simplified:

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

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

Expanded:

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

Factored:

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


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