Solve 2 * (m - 3) ^ 2 - 2(m + 2)(m - 4) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$2(m-3)^{2}-2(m+2)(m-4)$$

Evaluate

$34-8m$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(m-3\right)^{2}$.

$$2\left(m^{2}-6m+9\right)-2\left(m+2\right)\left(m-4\right)$$

Use the distributive property to multiply $2$ by $m^{2}-6m+9$.

$$2m^{2}-12m+18-2\left(m+2\right)\left(m-4\right)$$

Use the distributive property to multiply $-2$ by $m+2$.

$$2m^{2}-12m+18+\left(-2m-4\right)\left(m-4\right)$$

Use the distributive property to multiply $-2m-4$ by $m-4$ and combine like terms.

$$2m^{2}-12m+18-2m^{2}+4m+16$$

Combine $2m^{2}$ and $-2m^{2}$ to get $0$.

$$-12m+18+4m+16$$

Combine $-12m$ and $4m$ to get $-8m$.

$$-8m+18+16$$

Add $18$ and $16$ to get $34$.

$$-8m+34$$

Expand

$34-8m$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(m-3\right)^{2}$.

$$2\left(m^{2}-6m+9\right)-2\left(m+2\right)\left(m-4\right)$$

Use the distributive property to multiply $2$ by $m^{2}-6m+9$.

$$2m^{2}-12m+18-2\left(m+2\right)\left(m-4\right)$$

Use the distributive property to multiply $-2$ by $m+2$.

$$2m^{2}-12m+18+\left(-2m-4\right)\left(m-4\right)$$

Use the distributive property to multiply $-2m-4$ by $m-4$ and combine like terms.

$$2m^{2}-12m+18-2m^{2}+4m+16$$

Combine $2m^{2}$ and $-2m^{2}$ to get $0$.

$$-12m+18+4m+16$$

Combine $-12m$ and $4m$ to get $-8m$.

$$-8m+18+16$$

Add $18$ and $16$ to get $34$.

$$-8m+34$$