Solve (a+4)^2+2(a-3)(a-2)

$$( a + 4 ) ^ { 2 } + 2 ( a - 3 ) ( a - 2 )$$

Evaluate

$$3a^{2}-2a+28$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+4\right)^{2}.

$$a^{2}+8a+16+2\left(a-3\right)\left(a-2\right)$$

Use the distributive property to multiply 2 by a-3.

$$a^{2}+8a+16+\left(2a-6\right)\left(a-2\right)$$

Use the distributive property to multiply 2a-6 by a-2 and combine like terms.

$$a^{2}+8a+16+2a^{2}-10a+12$$

Combine a^{2} and 2a^{2} to get 3a^{2}.

$$3a^{2}+8a+16-10a+12$$

Combine 8a and -10a to get -2a.

$$3a^{2}-2a+16+12$$

Add 16 and 12 to get 28.

$$3a^{2}-2a+28$$

Expand

$$3a^{2}-2a+28$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+4\right)^{2}.

$$a^{2}+8a+16+2\left(a-3\right)\left(a-2\right)$$

Use the distributive property to multiply 2 by a-3.

$$a^{2}+8a+16+\left(2a-6\right)\left(a-2\right)$$

Use the distributive property to multiply 2a-6 by a-2 and combine like terms.

$$a^{2}+8a+16+2a^{2}-10a+12$$

Combine a^{2} and 2a^{2} to get 3a^{2}.

$$3a^{2}+8a+16-10a+12$$

Combine 8a and -10a to get -2a.

$$3a^{2}-2a+16+12$$

Add 16 and 12 to get 28.

$$3a^{2}-2a+28$$