Solve (a-6)^2+2(a-6)(a+4)+(a+4)^2

$$( a - 6 ) ^ { 2 } + 2 ( a - 6 ) ( a + 4 ) + ( a + 4 ) ^ { 2 }$$

Evaluate

$$4\left(a-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-6\right)^{2}.

$$a^{2}-12a+36+2\left(a-6\right)\left(a+4\right)+\left(a+4\right)^{2}$$

Use the distributive property to multiply 2 by a-6.

$$a^{2}-12a+36+\left(2a-12\right)\left(a+4\right)+\left(a+4\right)^{2}$$

Use the distributive property to multiply 2a-12 by a+4 and combine like terms.

$$a^{2}-12a+36+2a^{2}-4a-48+\left(a+4\right)^{2}$$

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

$$3a^{2}-12a+36-4a-48+\left(a+4\right)^{2}$$

Combine -12a and -4a to get -16a.

$$3a^{2}-16a+36-48+\left(a+4\right)^{2}$$

Subtract 48 from 36 to get -12.

$$3a^{2}-16a-12+\left(a+4\right)^{2}$$

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

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

Combine 3a^{2} and a^{2} to get 4a^{2}.

$$4a^{2}-16a-12+8a+16$$

Combine -16a and 8a to get -8a.

$$4a^{2}-8a-12+16$$

Add -12 and 16 to get 4.

$$4a^{2}-8a+4$$

Expand

$$4a^{2}-8a+4$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-6\right)^{2}.

$$a^{2}-12a+36+2\left(a-6\right)\left(a+4\right)+\left(a+4\right)^{2}$$

Use the distributive property to multiply 2 by a-6.

$$a^{2}-12a+36+\left(2a-12\right)\left(a+4\right)+\left(a+4\right)^{2}$$

Use the distributive property to multiply 2a-12 by a+4 and combine like terms.

$$a^{2}-12a+36+2a^{2}-4a-48+\left(a+4\right)^{2}$$

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

$$3a^{2}-12a+36-4a-48+\left(a+4\right)^{2}$$

Combine -12a and -4a to get -16a.

$$3a^{2}-16a+36-48+\left(a+4\right)^{2}$$

Subtract 48 from 36 to get -12.

$$3a^{2}-16a-12+\left(a+4\right)^{2}$$

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

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

Combine 3a^{2} and a^{2} to get 4a^{2}.

$$4a^{2}-16a-12+8a+16$$

Combine -16a and 8a to get -8a.

$$4a^{2}-8a-12+16$$

Add -12 and 16 to get 4.

$$4a^{2}-8a+4$$