Algebra - Expanding

"Expanding" ways removing the ( ) ... simply we have to do it the right way!

( ) are chosen "parentheses" or "brackets"

Any is within the ( ) needs to exist treated every bit a "package".

So when multiplying: multiply past everything inside the "package".

Case: Expand 3 × (v+2)

Answer:

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

Information technology is now expanded.

Nosotros can also complete the calculation:

3 × (v+two) = three × five + 3 × 2
= 15 + 6
= 21

In Algebra

In Algebra putting two things next to each other usually means to multiply.

And then 3(a+b) means to multiply 3 by (a+b)

Here is an example of expanding, using variables a, b and c instead of numbers:

And here is another example involving some numbers. Notice the "·" between the three and 6 to mean multiply, so three·six = 18:

Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying 2 negatives gives a positive:

In that case −three · -5 = +15 (a positive respond), simply here is an example where the 2d part is negative:

So the second term ended upward negative because 2x · −a = −2ax, (it is also neater to write "−2ax" rather than "−2xa").

That was as well interesting because of 10 being squared (x2)

Lastly, we take an example with three terms inside:

The aforementioned rule applies: multiply past everything inside the ().

And here is a hint: when a multiplication is obvious (like a · two) practise it direct abroad, but when information technology needs more thought (similar a · −b) exit it for the next line.

Many Times Many

How do we practice something like this?

(x + 2y)(3x − 4y)

Read Multiplying Polynomialsto find out!

Conclusion

Multiply by everything within the ()

Do information technology in two stages:

  • Write down the multiplications
  • Then practise the multiplications