Solve (2x - 3)(x - 1) and (- 2x + 1); (- 2x + 1)(2 - x) | 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

$$( 2 x - 3 ) \cdot ( x - 1 ) ( - 2 x + 1 ) \cdot ( - 2 x ) + 1 ( - 2 x )$$

Evaluate

$2x\left(4x^{3}-12x^{2}+11x-4\right)$

Solution Steps

Apply the distributive property by multiplying each term of $2x-3$ by each term of $x-1$.

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

Combine $-2x$ and $-3x$ to get $-5x$.

$$\left(2x^{2}-5x+3\right)\left(-2x+1\right)\left(-2\right)x+1\left(-2\right)x$$

Apply the distributive property by multiplying each term of $2x^{2}-5x+3$ by each term of $-2x+1$.

$$\left(-4x^{3}+2x^{2}+10x^{2}-5x-6x+3\right)\left(-2\right)x+1\left(-2\right)x$$

Combine $2x^{2}$ and $10x^{2}$ to get $12x^{2}$.

$$\left(-4x^{3}+12x^{2}-5x-6x+3\right)\left(-2\right)x+1\left(-2\right)x$$

Combine $-5x$ and $-6x$ to get $-11x$.

$$\left(-4x^{3}+12x^{2}-11x+3\right)\left(-2\right)x+1\left(-2\right)x$$

Use the distributive property to multiply $-4x^{3}+12x^{2}-11x+3$ by $-2$.

$$\left(8x^{3}-24x^{2}+22x-6\right)x+1\left(-2\right)x$$

Use the distributive property to multiply $8x^{3}-24x^{2}+22x-6$ by $x$.

$$8x^{4}-24x^{3}+22x^{2}-6x+1\left(-2\right)x$$

Multiply $1$ and $-2$ to get $-2$.

$$8x^{4}-24x^{3}+22x^{2}-6x-2x$$

Combine $-6x$ and $-2x$ to get $-8x$.

$$8x^{4}-24x^{3}+22x^{2}-8x$$

Expand

$8x^{4}-24x^{3}+22x^{2}-8x$

Solution Steps

Apply the distributive property by multiplying each term of $2x-3$ by each term of $x-1$.

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

Combine $-2x$ and $-3x$ to get $-5x$.

$$\left(2x^{2}-5x+3\right)\left(-2x+1\right)\left(-2\right)x+1\left(-2\right)x$$

Apply the distributive property by multiplying each term of $2x^{2}-5x+3$ by each term of $-2x+1$.

$$\left(-4x^{3}+2x^{2}+10x^{2}-5x-6x+3\right)\left(-2\right)x+1\left(-2\right)x$$

Combine $2x^{2}$ and $10x^{2}$ to get $12x^{2}$.

$$\left(-4x^{3}+12x^{2}-5x-6x+3\right)\left(-2\right)x+1\left(-2\right)x$$

Combine $-5x$ and $-6x$ to get $-11x$.

$$\left(-4x^{3}+12x^{2}-11x+3\right)\left(-2\right)x+1\left(-2\right)x$$

Use the distributive property to multiply $-4x^{3}+12x^{2}-11x+3$ by $-2$.

$$\left(8x^{3}-24x^{2}+22x-6\right)x+1\left(-2\right)x$$

Use the distributive property to multiply $8x^{3}-24x^{2}+22x-6$ by $x$.

$$8x^{4}-24x^{3}+22x^{2}-6x+1\left(-2\right)x$$

Multiply $1$ and $-2$ to get $-2$.

$$8x^{4}-24x^{3}+22x^{2}-6x-2x$$

Combine $-6x$ and $-2x$ to get $-8x$.

$$8x^{4}-24x^{3}+22x^{2}-8x$$