Question

what is(x+a) (x+b)=
(a+b)^3=
(a-b)^3=
​

Answer 1

Step-by-step explanation:

What is the formula of (a+b)3 ?

On your paper, draw yourself a copy of Pascal’s Triangle. Even if you don’t remember the name. Start with the number 1, then start and end each new row with 1’s, and for in-between numbers, add the two numbers above it.

Row 0: 1

Row 1: 1 1

Row 2: 1 2 1

Row 3: 1 3 3 1

Row 4: 1 4 6 4 1

Row 5: 1 5 10 10 5 1

These rows represent the exponent for our binomial, (a+b):

(a+b)0

(a+b)1

(a+b)2

(a+b)3

etc.

We want to cube (a+b), so look at “Row 3”, the row in which 3 is the second number:

1, 3, 3, 1

These are the coefficients for our ab terms.

Now, write down ab four times (one more than the exponent)

ab ab ab ab

Next, let’s write down the exponents for a, going from 3 down to 0

a³b a²b a¹b aºb

Then, we add the exponents for b, going from 0 up to 3

a³bº a²b¹ a¹b² aºb³

Since a and b are both positive, all of our signs are positive

a³bº + a²b¹ + a¹b² + aºb³

Finally, go back to our triangle, to the values 1 3 3 1. Put those values before each term.

1a³bº + 3a²b¹ + 3a¹b² + 1aºb³

But we can erase the “1” coefficients (because 1x is the same as x); erase the “1” exponents (because x¹ is the same as x), and delete the zero power with its letter letter (because xº is the same as 1):

a³ + 3a²b + 3ab² + b³

Practice this a few times, and it will become easier, and you’ll discover that you don’t need to read all these steps. You’ll do it all pretty easily. The hard part will be when you are raising (6x-7y) to a power because you have to remember to square and cube those entire terms, which will also change half the signs.