Solve (a+1)(a+2)+(a+3)(a+4)

$$( a + 1 ) ( a + 2 ) + ( a + 3 ) ( a + 4 )$$

Evaluate

$$2\left(a^{2}+5a+7\right)$$

Solution Steps

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

$$a^{2}+2a+a+2+\left(a+3\right)\left(a+4\right)$$

Combine 2a and a to get 3a.

$$a^{2}+3a+2+\left(a+3\right)\left(a+4\right)$$

Apply the distributive property by multiplying each term of a+3 by each term of a+4.

$$a^{2}+3a+2+a^{2}+4a+3a+12$$

Combine 4a and 3a to get 7a.

$$a^{2}+3a+2+a^{2}+7a+12$$

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

$$2a^{2}+3a+2+7a+12$$

Combine 3a and 7a to get 10a.

$$2a^{2}+10a+2+12$$

Add 2 and 12 to get 14.

$$2a^{2}+10a+14$$

Expand

$$2a^{2}+10a+14$$

Solution Steps

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

$$a^{2}+2a+a+2+\left(a+3\right)\left(a+4\right)$$

Combine 2a and a to get 3a.

$$a^{2}+3a+2+\left(a+3\right)\left(a+4\right)$$

Apply the distributive property by multiplying each term of a+3 by each term of a+4.

$$a^{2}+3a+2+a^{2}+4a+3a+12$$

Combine 4a and 3a to get 7a.

$$a^{2}+3a+2+a^{2}+7a+12$$

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

$$2a^{2}+3a+2+7a+12$$

Combine 3a and 7a to get 10a.

$$2a^{2}+10a+2+12$$

Add 2 and 12 to get 14.

$$2a^{2}+10a+14$$