Solve (v ) 9 * (x - 1) ^ 2 - 16 * (x + 2) ^ 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

$$9 ( x - 1 ) ^ { 2 } - 16 ( x + 2 ) ^ { 2 }$$

Evaluate

$-\left(x+11\right)\left(7x+5\right)$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-1\right)^{2}$.

$$9\left(x^{2}-2x+1\right)-16\left(x+2\right)^{2}$$

Use the distributive property to multiply $9$ by $x^{2}-2x+1$.

$$9x^{2}-18x+9-16\left(x+2\right)^{2}$$

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

$$9x^{2}-18x+9-16\left(x^{2}+4x+4\right)$$

Use the distributive property to multiply $-16$ by $x^{2}+4x+4$.

$$9x^{2}-18x+9-16x^{2}-64x-64$$

Combine $9x^{2}$ and $-16x^{2}$ to get $-7x^{2}$.

$$-7x^{2}-18x+9-64x-64$$

Combine $-18x$ and $-64x$ to get $-82x$.

$$-7x^{2}-82x+9-64$$

Subtract $64$ from $9$ to get $-55$.

$$-7x^{2}-82x-55$$

Expand

$-7x^{2}-82x-55$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-1\right)^{2}$.

$$9\left(x^{2}-2x+1\right)-16\left(x+2\right)^{2}$$

Use the distributive property to multiply $9$ by $x^{2}-2x+1$.

$$9x^{2}-18x+9-16\left(x+2\right)^{2}$$

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

$$9x^{2}-18x+9-16\left(x^{2}+4x+4\right)$$

Use the distributive property to multiply $-16$ by $x^{2}+4x+4$.

$$9x^{2}-18x+9-16x^{2}-64x-64$$

Combine $9x^{2}$ and $-16x^{2}$ to get $-7x^{2}$.

$$-7x^{2}-18x+9-64x-64$$

Combine $-18x$ and $-64x$ to get $-82x$.

$$-7x^{2}-82x+9-64$$

Subtract $64$ from $9$ to get $-55$.

$$-7x^{2}-82x-55$$