Solve 4 * (x - 1) ^ 2 - (2x - 1) ^ 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

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

Evaluate

$3-4x$

Solution Steps

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

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

Use the distributive property to multiply $4$ by $x^{2}-2x+1$.

$$4x^{2}-8x+4-\left(2x-1\right)^{2}$$

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

$$4x^{2}-8x+4-\left(4x^{2}-4x+1\right)$$

To find the opposite of $4x^{2}-4x+1$, find the opposite of each term.

$$4x^{2}-8x+4-4x^{2}+4x-1$$

Combine $4x^{2}$ and $-4x^{2}$ to get $0$.

$$-8x+4+4x-1$$

Combine $-8x$ and $4x$ to get $-4x$.

$$-4x+4-1$$

Subtract $1$ from $4$ to get $3$.

$$-4x+3$$

Expand

$3-4x$

Solution Steps

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

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

Use the distributive property to multiply $4$ by $x^{2}-2x+1$.

$$4x^{2}-8x+4-\left(2x-1\right)^{2}$$

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

$$4x^{2}-8x+4-\left(4x^{2}-4x+1\right)$$

To find the opposite of $4x^{2}-4x+1$, find the opposite of each term.

$$4x^{2}-8x+4-4x^{2}+4x-1$$

Combine $4x^{2}$ and $-4x^{2}$ to get $0$.

$$-8x+4+4x-1$$

Combine $-8x$ and $4x$ to get $-4x$.

$$-4x+4-1$$

Subtract $1$ from $4$ to get $3$.

$$-4x+3$$