Solve (2x - 3)(5x - 1) - (2x - 3)(x + 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

$$(2x-3)(5x-1)-(2x-3)(x+1)$$

Evaluate

$8x^{2}-16x+6$

Solution Steps

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

$$10x^{2}-2x-15x+3-\left(2x-3\right)\left(x+1\right)$$

Combine $-2x$ and $-15x$ to get $-17x$.

$$10x^{2}-17x+3-\left(2x-3\right)\left(x+1\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}+2x-3x-3\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}-x-3\right)$$

To find the opposite of $2x^{2}-x-3$, find the opposite of each term.

$$10x^{2}-17x+3-2x^{2}-\left(-x\right)-\left(-3\right)$$

The opposite of $-x$ is $x$.

$$10x^{2}-17x+3-2x^{2}+x-\left(-3\right)$$

The opposite of $-3$ is $3$.

$$10x^{2}-17x+3-2x^{2}+x+3$$

Combine $10x^{2}$ and $-2x^{2}$ to get $8x^{2}$.

$$8x^{2}-17x+3+x+3$$

Combine $-17x$ and $x$ to get $-16x$.

$$8x^{2}-16x+3+3$$

Add $3$ and $3$ to get $6$.

$$8x^{2}-16x+6$$

Expand

$8x^{2}-16x+6$

Solution Steps

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

$$10x^{2}-2x-15x+3-\left(2x-3\right)\left(x+1\right)$$

Combine $-2x$ and $-15x$ to get $-17x$.

$$10x^{2}-17x+3-\left(2x-3\right)\left(x+1\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}+2x-3x-3\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}-x-3\right)$$

To find the opposite of $2x^{2}-x-3$, find the opposite of each term.

$$10x^{2}-17x+3-2x^{2}-\left(-x\right)-\left(-3\right)$$

The opposite of $-x$ is $x$.

$$10x^{2}-17x+3-2x^{2}+x-\left(-3\right)$$

The opposite of $-3$ is $3$.

$$10x^{2}-17x+3-2x^{2}+x+3$$

Combine $10x^{2}$ and $-2x^{2}$ to get $8x^{2}$.

$$8x^{2}-17x+3+x+3$$

Combine $-17x$ and $x$ to get $-16x$.

$$8x^{2}-16x+3+3$$

Add $3$ and $3$ to get $6$.

$$8x^{2}-16x+6$$