Solve 7^2(a+1)^2-2(a-1)(a+2)

$$7 ^ { 2 } ( a + 1 ) ^ { 2 } - 2 ( a - 1 ) ( a + 2 )$$

Evaluate

$$47a^{2}+96a+53$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$49\left(a+1\right)^{2}-2\left(a-1\right)\left(a+2\right)$$

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

$$49\left(a^{2}+2a+1\right)-2\left(a-1\right)\left(a+2\right)$$

Use the distributive property to multiply 49 by a^{2}+2a+1.

$$49a^{2}+98a+49-2\left(a-1\right)\left(a+2\right)$$

Use the distributive property to multiply -2 by a-1.

$$49a^{2}+98a+49+\left(-2a+2\right)\left(a+2\right)$$

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

$$49a^{2}+98a+49-2a^{2}-2a+4$$

Combine 49a^{2} and -2a^{2} to get 47a^{2}.

$$47a^{2}+98a+49-2a+4$$

Combine 98a and -2a to get 96a.

$$47a^{2}+96a+49+4$$

Add 49 and 4 to get 53.

$$47a^{2}+96a+53$$

Expand

$$47a^{2}+96a+53$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$49\left(a+1\right)^{2}-2\left(a-1\right)\left(a+2\right)$$

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

$$49\left(a^{2}+2a+1\right)-2\left(a-1\right)\left(a+2\right)$$

Use the distributive property to multiply 49 by a^{2}+2a+1.

$$49a^{2}+98a+49-2\left(a-1\right)\left(a+2\right)$$

Use the distributive property to multiply -2 by a-1.

$$49a^{2}+98a+49+\left(-2a+2\right)\left(a+2\right)$$

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

$$49a^{2}+98a+49-2a^{2}-2a+4$$

Combine 49a^{2} and -2a^{2} to get 47a^{2}.

$$47a^{2}+98a+49-2a+4$$

Combine 98a and -2a to get 96a.

$$47a^{2}+96a+49+4$$

Add 49 and 4 to get 53.

$$47a^{2}+96a+53$$