Solve {l}{4(a+2)^2-7(a+3)(a-3)}{+3(a-1)^2}

$$\left. \begin{array} { l } { 4 ( a + 2 ) ^ { 2 } - 7 ( a + 3 ) ( a - 3 ) } \\ { + 3 ( a - 1 ) ^ { 2 } } \end{array} \right.$$

Evaluate

$$10a+82$$

Solution Steps

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

$$4\left(a^{2}+4a+4\right)-7\left(a+3\right)\left(a-3\right)+3\left(a-1\right)^{2}$$

Use the distributive property to multiply 4 by a^{2}+4a+4.

$$4a^{2}+16a+16-7\left(a+3\right)\left(a-3\right)+3\left(a-1\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$4a^{2}+16a+16-7\left(a+3\right)\left(a-3\right)+3\left(a^{2}-2a+1\right)$$

Use the distributive property to multiply 3 by a^{2}-2a+1.

$$4a^{2}+16a+16-7\left(a+3\right)\left(a-3\right)+3a^{2}-6a+3$$

Use the distributive property to multiply -7 by a+3.

$$4a^{2}+16a+16+\left(-7a-21\right)\left(a-3\right)+3a^{2}-6a+3$$

Use the distributive property to multiply -7a-21 by a-3 and combine like terms.

$$4a^{2}+16a+16-7a^{2}+63+3a^{2}-6a+3$$

Combine 4a^{2} and -7a^{2} to get -3a^{2}.

$$-3a^{2}+16a+16+63+3a^{2}-6a+3$$

Add 16 and 63 to get 79.

$$-3a^{2}+16a+79+3a^{2}-6a+3$$

Combine -3a^{2} and 3a^{2} to get 0.

$$16a+79-6a+3$$

Combine 16a and -6a to get 10a.

$$10a+79+3$$

Add 79 and 3 to get 82.

$$10a+82$$

Expand

$$10a+82$$

Solution Steps

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

$$4\left(a^{2}+4a+4\right)-7\left(a+3\right)\left(a-3\right)+3\left(a-1\right)^{2}$$

Use the distributive property to multiply 4 by a^{2}+4a+4.

$$4a^{2}+16a+16-7\left(a+3\right)\left(a-3\right)+3\left(a-1\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$4a^{2}+16a+16-7\left(a+3\right)\left(a-3\right)+3\left(a^{2}-2a+1\right)$$

Use the distributive property to multiply 3 by a^{2}-2a+1.

$$4a^{2}+16a+16-7\left(a+3\right)\left(a-3\right)+3a^{2}-6a+3$$

Use the distributive property to multiply -7 by a+3.

$$4a^{2}+16a+16+\left(-7a-21\right)\left(a-3\right)+3a^{2}-6a+3$$

Use the distributive property to multiply -7a-21 by a-3 and combine like terms.

$$4a^{2}+16a+16-7a^{2}+63+3a^{2}-6a+3$$

Combine 4a^{2} and -7a^{2} to get -3a^{2}.

$$-3a^{2}+16a+16+63+3a^{2}-6a+3$$

Add 16 and 63 to get 79.

$$-3a^{2}+16a+79+3a^{2}-6a+3$$

Combine -3a^{2} and 3a^{2} to get 0.

$$16a+79-6a+3$$

Combine 16a and -6a to get 10a.

$$10a+79+3$$

Add 79 and 3 to get 82.

$$10a+82$$