Solve (3a+2)^2(3a-2)^2quadtext{(6)}999^2-1002*998

$$( 3 a + 2 ) ^ { 2 } ( 3 a - 2 ) ^ { 2 } \quad \text { (6) } 999 ^ { 2 } - 1002 \times 998$$

Evaluate

$$5988006\left(9a^{2}-4\right)^{2}-999996$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+2\right)^{2}.

$$\left(9a^{2}+12a+4\right)\left(3a-2\right)^{2}\times 6\times 999^{2}-1002\times 998$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-2\right)^{2}.

$$\left(9a^{2}+12a+4\right)\left(9a^{2}-12a+4\right)\times 6\times 999^{2}-1002\times 998$$

Calculate 999 to the power of 2 and get 998001.

$$\left(9a^{2}+12a+4\right)\left(9a^{2}-12a+4\right)\times 6\times 998001-1002\times 998$$

Multiply 6 and 998001 to get 5988006.

$$\left(9a^{2}+12a+4\right)\left(9a^{2}-12a+4\right)\times 5988006-1002\times 998$$

Use the distributive property to multiply 9a^{2}+12a+4 by 9a^{2}-12a+4 and combine like terms.

$$\left(81a^{4}-72a^{2}+16\right)\times 5988006-1002\times 998$$

Use the distributive property to multiply 81a^{4}-72a^{2}+16 by 5988006.

$$485028486a^{4}-431136432a^{2}[phone]\times 998$$

Multiply 1002 and 998 to get 999996.

$$485028486a^{4}-431136432a^{2}[phone]$$

Subtract 999996 from 95808096 to get 94808100.

$$485028486a^{4}-431136432a^{2}[phone]$$

Expand

$$485028486a^{4}-431136432a^{2}[phone]$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+2\right)^{2}.

$$\left(9a^{2}+12a+4\right)\left(3a-2\right)^{2}\times 6\times 999^{2}-1002\times 998$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-2\right)^{2}.

$$\left(9a^{2}+12a+4\right)\left(9a^{2}-12a+4\right)\times 6\times 999^{2}-1002\times 998$$

Calculate 999 to the power of 2 and get 998001.

$$\left(9a^{2}+12a+4\right)\left(9a^{2}-12a+4\right)\times 6\times 998001-1002\times 998$$

Multiply 6 and 998001 to get 5988006.

$$\left(9a^{2}+12a+4\right)\left(9a^{2}-12a+4\right)\times 5988006-1002\times 998$$

Use the distributive property to multiply 9a^{2}+12a+4 by 9a^{2}-12a+4 and combine like terms.

$$\left(81a^{4}-72a^{2}+16\right)\times 5988006-1002\times 998$$

Use the distributive property to multiply 81a^{4}-72a^{2}+16 by 5988006.

$$485028486a^{4}-431136432a^{2}[phone]\times 998$$

Multiply 1002 and 998 to get 999996.

$$485028486a^{4}-431136432a^{2}[phone]$$

Subtract 999996 from 95808096 to get 94808100.

$$485028486a^{4}-431136432a^{2}[phone]$$