Help with Algebra questions!!!!!!!!!!!!!!!?

Question

how would you expand the following questions:
1) (2a+b)²=
2) (2a-b)²=
3) (2a+b)³=
4) (2a-b)³=

Answer 1

The exponents mean multiply the thing in between the () by itself that number of times, so for the first one

(2a+b)(2a+b)

and for the last one

(2a-b)(2a-b)(2a-b)

the next step is to multiply the individual terms by each other

So for the first one

2a*2a + 2ab + 2ab + b² = 4a² +4ab + b²

Answer 2

Use Pascal Law.

Let say (a + b)^n
The coefficient can be determined by this method as shown below:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
...
Note that '1's are the boundary while every number inside the pyramid is the sum of two numbers above them.

since (a + b)^n; thus corresponding coefficient should be taken from the nth row.

For example:
(a + b)^3;
by taking the coefficients in the 4th row;
=1(a^3) (b^0) + 3(a^2)(b^1) + 3(a^1)(b^2) + 1(a^0)(b^3).

Note that the power of a is decreasing from n which is 3 to 0 and vice versa as for b.
And the sum of the index(the power) of both variables are always equal to the n which is 3.

Your questions:
i)(2a+b)² = 1[(2a)^2](b^0) + 2[(2a)^1](b^1) + 1[(2a)^0](b^2) = 4a² + 4ab + b²

ii) (2a-b)² = 1[(2a)^2][(-b)^0] + 2[(2a)^1][(-b)^1]+ 1[(2a)^0][(-b)^2] = 4a² - 4ab + b²

iii) (2a+b)³ = 1[(2a)^3][b^0] + 3[(2a)^2][b^1] + 3[(2a)^1][b^2] + 1[(2a)^0][b^3] = 8a³ + 12a²b + 6ab² + b³

iv) (2a-b)³ = 1[(2a)^3][(-b)^0] + 3[(2a)^2][(-b)^1] + 3[(2a)^1][(-b)^2] + 1[(2a)^0][(-b)^3] = 8a³ - 12a²b + 6ab² - b³

Special trick only for (a + b)²
(a + b)² = a² + 2ab + b²;

Thus for your first two question:
i) (2a+b)² = (2a)² + 2(2a)(b) + b²
= 4a² + 4ab + b²

ii) (2a - b)² = (2a)² + 2(2a)(-b) + (-b)²
= 4a² - 4ab + b²

Happy trying

Answer 3

1) (2a + b ) x (2a + b ) = 4a^2 + 2ab + 2ab + b^2
= 4a^2 + 4ab + b^2

2) (2a - b ) x (2a - b ) = 2a^2 - 2ab - 2ab + b^2
= 2a^2 - 4ab + b^2

3) use number 1
(2a + b ) x ( 4a^2 + 4ab + b^2)
= 8a^3 + 8a^2b + 2ab^2 + 4a^2b + 4ab^2 + b^3
= 8a^3 +12a^2b + 6ab^2 + b^3

4) use number 2
( 2a - b ) x ( 2a^2 - 4ab + b^2 )
= 4a^3 - 8a^2b + 2ab^2 - 2a^2b + 4ab^2 - b^3
= 4a^3 -10a^2b + 6 ab^2 - b^3

Answer 4

1) 4a²+b²+4ab
2) 4a²+b²-4ab
3) (4a²+b²+4ab)(2a+b)
=8a³+b³+12a²b+6ab²
4) (4a²+b²-4ab)(2a-b)
=8a³-b³-12a²b+6ab²

Answer 5

1.4a^2+4ab+b^2

2.4a^2-4ab+b^2

3.8a^3+12a^2b+6ab^2+b^3

4.8a^3-12a^2b+6ab^2-b^3

Answer 6

1.THE ANSWER IS 4AB