Evaluate: (a^m-a^{m-1}+a^{m-2}) * (-2a)

Expression: $\left( {a}^{m}-{a}^{m-1}+{a}^{m-2} \right) \times \left( -2a \right)$

Multiply each term in the parentheses by $-2a$

$-{a}^{m} \times 2a-{a}^{m-1} \times \left( -2a \right)-{a}^{m-2} \times 2a$

Calculate the product

$-2{a}^{m+1}-{a}^{m-1} \times \left( -2a \right)-{a}^{m-2} \times 2a$

Multiplying two negatives equals a positive: $\left( - \right) \times \left( - \right)=\left( + \right)$

$-2{a}^{m+1}+{a}^{m-1} \times 2a-{a}^{m-2} \times 2a$

Calculate the product

$-2{a}^{m+1}+2{a}^{m}-{a}^{m-2} \times 2a$

Calculate the product

$-2{a}^{m+1}+2{a}^{m}-2{a}^{m-1}$