Solve (x ^ 2 - 4x) ^ 2 + 8(4x - x ^ 2) - 48 | 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

$$(x^{2}-4x)^{2}+8(4x-x^{2})-48$$

Evaluate

$\left(x-6\right)\left(x+2\right)\left(x-2\right)^{2}$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x^{2}-4x\right)^{2}$.

$$\left(x^{2}\right)^{2}-8x^{2}x+16x^{2}+8\left(4x-x^{2}\right)-48$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$x^{4}-8x^{2}x+16x^{2}+8\left(4x-x^{2}\right)-48$$

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$x^{4}-8x^{3}+16x^{2}+8\left(4x-x^{2}\right)-48$$

Use the distributive property to multiply $8$ by $4x-x^{2}$.

$$x^{4}-8x^{3}+16x^{2}+32x-8x^{2}-48$$

Combine $16x^{2}$ and $-8x^{2}$ to get $8x^{2}$.

$$x^{4}-8x^{3}+8x^{2}+32x-48$$

Expand

$x^{4}-8x^{3}+8x^{2}+32x-48$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x^{2}-4x\right)^{2}$.

$$\left(x^{2}\right)^{2}-8x^{2}x+16x^{2}+8\left(4x-x^{2}\right)-48$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$x^{4}-8x^{2}x+16x^{2}+8\left(4x-x^{2}\right)-48$$

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$x^{4}-8x^{3}+16x^{2}+8\left(4x-x^{2}\right)-48$$

Use the distributive property to multiply $8$ by $4x-x^{2}$.

$$x^{4}-8x^{3}+16x^{2}+32x-8x^{2}-48$$

Combine $16x^{2}$ and $-8x^{2}$ to get $8x^{2}$.

$$x^{4}-8x^{3}+8x^{2}+32x-48$$