Solve (a_{1}+d)(a_{1}+21d)

$$( a _ { 1 } + d ) ( a _ { 1 } + 21 d )$$

Expand

$$a_{1}^{2}+22a_{1}d+21d^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of a_{1}+d by each term of a_{1}+21d.

$$a_{1}^{2}+21a_{1}d+da_{1}+21d^{2}$$

Combine 21a_{1}d and da_{1} to get 22a_{1}d.

$$a_{1}^{2}+22a_{1}d+21d^{2}$$

Evaluate

$$\left(a_{1}+d\right)\left(a_{1}+21d\right)$$

Solution Steps

Apply the distributive property by multiplying each term of a_{1}+d by each term of a_{1}+21d.

$$a_{1}^{2}+21a_{1}d+da_{1}+21d^{2}$$

Combine 21a_{1}d and da_{1} to get 22a_{1}d.

$$a_{1}^{2}+22a_{1}d+21d^{2}$$