Solve 9 * (x - 1) ^ 2 - 4 * (2x + 3) ^ 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

$$9(x-1)^{2}-4(2x+3)^{2}$$

Evaluate

$-\left(x+9\right)\left(7x+3\right)$

Solution Steps

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

$$9\left(x^{2}-2x+1\right)-4\left(2x+3\right)^{2}$$

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

$$9x^{2}-18x+9-4\left(2x+3\right)^{2}$$

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

$$9x^{2}-18x+9-4\left(4x^{2}+12x+9\right)$$

Use the distributive property to multiply $-4$ by $4x^{2}+12x+9$.

$$9x^{2}-18x+9-16x^{2}-48x-36$$

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

$$-7x^{2}-18x+9-48x-36$$

Combine $-18x$ and $-48x$ to get $-66x$.

$$-7x^{2}-66x+9-36$$

Subtract $36$ from $9$ to get $-27$.

$$-7x^{2}-66x-27$$

Expand

$-7x^{2}-66x-27$

Solution Steps

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

$$9\left(x^{2}-2x+1\right)-4\left(2x+3\right)^{2}$$

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

$$9x^{2}-18x+9-4\left(2x+3\right)^{2}$$

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

$$9x^{2}-18x+9-4\left(4x^{2}+12x+9\right)$$

Use the distributive property to multiply $-4$ by $4x^{2}+12x+9$.

$$9x^{2}-18x+9-16x^{2}-48x-36$$

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

$$-7x^{2}-18x+9-48x-36$$

Combine $-18x$ and $-48x$ to get $-66x$.

$$-7x^{2}-66x+9-36$$

Subtract $36$ from $9$ to get $-27$.

$$-7x^{2}-66x-27$$