Solve (2y+3)(y-2)-(5y+3)(y-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

$$(2y+3)(y-2)-(5y+3)(y-2)$$

Evaluate

$-3y\left(y-2\right)$

Solution Steps

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

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

Combine $-4y$ and $3y$ to get $-y$.

$$2y^{2}-y-6-\left(5y+3\right)\left(y-2\right)$$

Apply the distributive property by multiplying each term of $5y+3$ by each term of $y-2$.

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

Combine $-10y$ and $3y$ to get $-7y$.

$$2y^{2}-y-6-\left(5y^{2}-7y-6\right)$$

To find the opposite of $5y^{2}-7y-6$, find the opposite of each term.

$$2y^{2}-y-6-5y^{2}-\left(-7y\right)-\left(-6\right)$$

The opposite of $-7y$ is $7y$.

$$2y^{2}-y-6-5y^{2}+7y-\left(-6\right)$$

The opposite of $-6$ is $6$.

$$2y^{2}-y-6-5y^{2}+7y+6$$

Combine $2y^{2}$ and $-5y^{2}$ to get $-3y^{2}$.

$$-3y^{2}-y-6+7y+6$$

Combine $-y$ and $7y$ to get $6y$.

$$-3y^{2}+6y-6+6$$

Add $-6$ and $6$ to get $0$.

$$-3y^{2}+6y$$

Expand

$6y-3y^{2}$

Solution Steps

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

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

Combine $-4y$ and $3y$ to get $-y$.

$$2y^{2}-y-6-\left(5y+3\right)\left(y-2\right)$$

Apply the distributive property by multiplying each term of $5y+3$ by each term of $y-2$.

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

Combine $-10y$ and $3y$ to get $-7y$.

$$2y^{2}-y-6-\left(5y^{2}-7y-6\right)$$

To find the opposite of $5y^{2}-7y-6$, find the opposite of each term.

$$2y^{2}-y-6-5y^{2}-\left(-7y\right)-\left(-6\right)$$

The opposite of $-7y$ is $7y$.

$$2y^{2}-y-6-5y^{2}+7y-\left(-6\right)$$

The opposite of $-6$ is $6$.

$$2y^{2}-y-6-5y^{2}+7y+6$$

Combine $2y^{2}$ and $-5y^{2}$ to get $-3y^{2}$.

$$-3y^{2}-y-6+7y+6$$

Combine $-y$ and $7y$ to get $6y$.

$$-3y^{2}+6y-6+6$$

Add $-6$ and $6$ to get $0$.

$$-3y^{2}+6y$$