Solve D ) ( 2a+ 3)(a+1)-(a+5)(a-2) 29 | 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

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

Evaluate

$a^{2}+2a+13$

Solution Steps

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

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

Combine $2a$ and $3a$ to get $5a$.

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

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

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

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

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

To find the opposite of $a^{2}+3a-10$, find the opposite of each term.

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

The opposite of $-10$ is $10$.

$$2a^{2}+5a+3-a^{2}-3a+10$$

Combine $2a^{2}$ and $-a^{2}$ to get $a^{2}$.

$$a^{2}+5a+3-3a+10$$

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

$$a^{2}+2a+3+10$$

Add $3$ and $10$ to get $13$.

$$a^{2}+2a+13$$

Expand

$a^{2}+2a+13$

Solution Steps

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

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

Combine $2a$ and $3a$ to get $5a$.

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

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

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

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

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

To find the opposite of $a^{2}+3a-10$, find the opposite of each term.

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

The opposite of $-10$ is $10$.

$$2a^{2}+5a+3-a^{2}-3a+10$$

Combine $2a^{2}$ and $-a^{2}$ to get $a^{2}$.

$$a^{2}+5a+3-3a+10$$

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

$$a^{2}+2a+3+10$$

Add $3$ and $10$ to get $13$.

$$a^{2}+2a+13$$