How do you expand brackets?

Answer 1

Expanding brackets in math is simply multiplying all expressions inside the bracket with the variable or coefficient outside.

For example:

3x(5 + 3y) = 2

To expand the brackets, simply multiply 3x with each of the expressions inside, always keeping in mind the sign of the answer (negative/positive)

Step 1: (3x * 5) + (3x * 3y) = 2

Step 2: 15x + 9xy = 2

Here is another example in which the signs change from negative to positive:

-3 (-2x + 4) = 1

Since you multiply -3 with -2x, you are multiplying a negative value with a negative value. Minus ( - ) and minus (-) multiply to give a positive value.

Step 1: (-3x * -2x) + (-3x * 4) = 1

Step 2: 6x - 12x = 1

You will notice that, in time, as you continue to practice with these types of questions, you will not be needing Step 1 and be able to skip to Step 2.

Another example, in the case where you have brackets^squared

3(2x + 5)^2 = 4

In this case, you cannot directly multiply 3 with the expressions in the bracket since they are being squared and must be evaluated first. In the case where you have a polynomial which is being squared, you must expand it first using the rule:

Note: ^2 means squared (Just like 5^2 = 25)

(a + b)^2 = a^2 + 2ab + b^2

[Where a and b may be any value which cannot be solved directly using arithmetic]

So in the case above you use this rule. 2x is 'a' and '5' is b.

3(2x + 5)^2 = 4

3(4x^2 + 2(2x)(5) + (5)^2) = 4

3(4x^2 + 20x + 25) = 4

At this point, you may multiply the brackets, since the term inside has been fully expanded.

(3 * 4x^2) + (3 * 20x) + (3 * 25) = 4

12x^2 + 60x + 75 = 4

You have successfully expanded the brackets at this point =D.

In the case where you have two brackets:

(a + b)(b + c) = 3

You must multiply each term in bracket #2 with each term in bracket #1.

Start with multiplying a with b and c, then b with b and c.

(a*b) + (a*c) + (b*b) + (b*c) = 3

ab + ab + bb + bc = 3

Hope this helps...