Solve (x-1)\times-4(1-2x)+(1-2x)^(2)(1) | 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

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

Evaluate

$\left(1-2x\right)\left(5-6x\right)$

Solution Steps

Use the distributive property to multiply $x-1$ by $-4$.

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

Use the distributive property to multiply $-4x+4$ by $1-2x$ and combine like terms.

$$-12x+8x^{2}+4+\left(1-2x\right)^{2}\times 1$$

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

$$-12x+8x^{2}+4+\left(1-4x+4x^{2}\right)\times 1$$

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

$$-12x+8x^{2}+4+1-4x+4x^{2}$$

Add $4$ and $1$ to get $5$.

$$-12x+8x^{2}+5-4x+4x^{2}$$

Combine $-12x$ and $-4x$ to get $-16x$.

$$-16x+8x^{2}+5+4x^{2}$$

Combine $8x^{2}$ and $4x^{2}$ to get $12x^{2}$.

$$-16x+12x^{2}+5$$

Expand

$12x^{2}-16x+5$

Solution Steps

Use the distributive property to multiply $x-1$ by $-4$.

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

Use the distributive property to multiply $-4x+4$ by $1-2x$ and combine like terms.

$$-12x+8x^{2}+4+\left(1-2x\right)^{2}\times 1$$

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

$$-12x+8x^{2}+4+\left(1-4x+4x^{2}\right)\times 1$$

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

$$-12x+8x^{2}+4+1-4x+4x^{2}$$

Add $4$ and $1$ to get $5$.

$$-12x+8x^{2}+5-4x+4x^{2}$$

Combine $-12x$ and $-4x$ to get $-16x$.

$$-16x+8x^{2}+5+4x^{2}$$

Combine $8x^{2}$ and $4x^{2}$ to get $12x^{2}$.

$$-16x+12x^{2}+5$$