Solve មុខវិជ្ជា: ច័ន្ទ ពុធ ព្រហ សុក្រ សៅរ៍ 9 * (x - 1) ^ 2 - varphi * (2x - 3) ^ 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

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

Evaluate

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

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 $30x$.

$$-7x^{2}+30x+9-36$$

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

$$-7x^{2}+30x-27$$

Expand

$-7x^{2}+30x-27$

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 $30x$.

$$-7x^{2}+30x+9-36$$

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

$$-7x^{2}+30x-27$$