Solve - 4 * (x - 5) ^ 2 + 2(x + 2)(x - 2) | 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

$$-4(x-5)^{2}+2(x+2)(x-2)$$

Evaluate

$-2x^{2}+40x-108$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-5\right)^{2}$.

$$-4\left(x^{2}-10x+25\right)+2\left(x+2\right)\left(x-2\right)$$

Use the distributive property to multiply $-4$ by $x^{2}-10x+25$.

$$-4x^{2}+40x-100+2\left(x+2\right)\left(x-2\right)$$

Use the distributive property to multiply $2$ by $x+2$.

$$-4x^{2}+40x-100+\left(2x+4\right)\left(x-2\right)$$

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

$$-4x^{2}+40x-100+2x^{2}-8$$

Combine $-4x^{2}$ and $2x^{2}$ to get $-2x^{2}$.

$$-2x^{2}+40x-100-8$$

Subtract $8$ from $-100$ to get $-108$.

$$-2x^{2}+40x-108$$

Expand

$-2x^{2}+40x-108$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-5\right)^{2}$.

$$-4\left(x^{2}-10x+25\right)+2\left(x+2\right)\left(x-2\right)$$

Use the distributive property to multiply $-4$ by $x^{2}-10x+25$.

$$-4x^{2}+40x-100+2\left(x+2\right)\left(x-2\right)$$

Use the distributive property to multiply $2$ by $x+2$.

$$-4x^{2}+40x-100+\left(2x+4\right)\left(x-2\right)$$

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

$$-4x^{2}+40x-100+2x^{2}-8$$

Combine $-4x^{2}$ and $2x^{2}$ to get $-2x^{2}$.

$$-2x^{2}+40x-100-8$$

Subtract $8$ from $-100$ to get $-108$.

$$-2x^{2}+40x-108$$