OK I remember F.O.I.L but how do you do it when it is (a^2+2a+1)(a+1)?

Answer 1

You multiply each term in first by each in the second... essentially what FOIL is doing.

So,
a^2 * a = a^3
a^2 * 1 = a^2

2a * a = 2a^2
2a * 1 = 2a

1 * a = a
1 * 1 = 1

So your new equation is
a^3 + a^2 + 2a^2 + 2a + a + 1

Combining like terms, your final answer will be
a^3 + 3a^2 + 3a + 1

Answer 2

FOIL stands for First, Outer, Inner, and Last. It really only applies to 2-term multipliers. With
(a^2 + 2a + 1) (a + 1) you have to distribute the (a + 1). You CAN regroup (a^2 + 2a + 1) as
(a^2 + 2a) + 1 and then distribute (a + 1) to get
(a^2 + 2a)(a + 1) + 1(a + 1), and then apply FOIL,
a^3 + a^2 + 2a^2 + 2a + a + 1 =
a^3 + 3a^2 + 3a + 1
or you can simply distribute (a + 1):
a^2(a + 1) + 2a(a + 1) + 1(a + 1), and then distribute the leading terms:
(a*a^2 + a^2) + (2a*a + 2a) + a + 1, giving
a^3 + a^2 + 2a^2 + 2a + a + 1 =
a^3 + 3a^2 + 3a + 1

Answer 3

It's the same concept as F.O.I.L., but you do another multiplication.

(a^2 + 2a + 1)(a + 1)

=> a^2(a) + 2a(a) + 1(a) + a^2(1) + 2a(1) + 1(1)
=> a^3 + 2a^2 + a + a^2 + 2a + 1
=> a^3 + 3a^2 + 3a + 1

So, a^3 + 3a^2 + 3a + 1 is your solution

Answer 4

I always did these with the box method or I'd get confused. Draw a box with three columns and 2 rows. Along the top, put a^2 on top of column 1, +2a on column 2 and +1 on the last column. Down the side, put a beside row 1 and +1 beside the second row. Then for each box, multiply the row and column and write it in that box. Then just add everything up for your answer.

Hope this helps:
..........a^2.....+2a.......+1
a........a^3......2a^2......a
+1......a^2.......2a.........1

a^3 + 2a^2 + a^2 + 2a + a + 1
a^3 + 3a^2 + 3a + 1

Answer 5

(a^2 * a) + (a^2 * 1) + (2a * a) + (2a * 1) + (1 * a) + (1 * 1)

= a^3 + a^2 + 2a^2 + 2a + a + 1

= a^3 + 3a^2 + 3a + 1

Answer 6

(a^2+2a+1)(a+1)?

(a^3+2a^2+a+a^2+2a+1)

first multiply first bracet with a and then 1

a^3+3a^2+3a+1

Answer 7

(a^2+2a+1)(a+1)
(a^2+2a+1)=(a+1)^2
(a+1)^2(a+1)=(a+1)^3
Use binomial theorem.
a^3+3a^2+3a+1

Answer 8

a^3+3a^2+3a+1