Sign Change for Multiplication!

Some of you might not have caught algebra well. Maths sometimes is as simple as spotting a pattern.

2(a) = 2a
b(3c) = 3bc
5d(3ek) = 15dek
Spot any pattern?

2(a) = 2 × a = 2a
b(3c) = b × 3c = 3bc
5d(3ek) = 5d × 3ek = 15dek
That was simple enough?

Let's get to what is usually tested:
Q1. 2(a + b) = 2a + 2b
Q2. 3(c + 4d) = 3c + 12d

Let's get to the part where lots of mistakes occur! When you see a negative sign, you have to check for? SIGN CHANGE!

(+)(+) = (+) <-- Do not need to check for sign change because you do not see the negative sign!
(-)(-) = (+)
--------------------
(+)(-) = (-)
(-)(+) = (-)

Q3. 5(f - 2g) = 5f - 10g
Why is it -10g? This is because of +5 × (-2g) = -10g.

Q4. -5(f - 2g) = -5f + 10g
Why is it -5f? This is because of -5 × (+f) = -5f.
Why is it +10g? This is because of -5 × (-2g) = +10g.

Q5. -5(-f - 2g) = 5f + 10g
Why is it -5f? This is because of -5 × (-f) = +5f.
Why is it +10g? This is because of -5 × (-2g) = +10g.

Let's try something longer:
Q6. 3(-2h + 5k - 7m) = -6h + 15k - 21m
Why is it -6h? This is because of 3 × (-2h) = -6h.
Why is it +15k? This is because of 3 × (+5k) = +15k.
Why is it -21m? This is because of 3 × (-7m) = -21m.

Q7. -3(-2h + 5k - 7m) = 6h - 15k + 21m
Why is it -6h? This is because of -3 × (-2h) = +6h.
Why is it +15k? This is because of -3 × (+5k) = -15k.
Why is it -21m? This is because of -3 × (-7m) = +21m.

Q8. -3(-2h + 5ka - 7mn) = 6h - 15ka + 21mn
Why is it -6h? This is because of -3 × (-2h) = +6h.
Why is it +15k? This is because of -3 × (+5ka) = -15ka.
Why is it -21m? This is because of -3 × (-7mn) = +21mn.

Remembered we did index notation?
a × a = a²
Some of you might wonder why not just write a × a = aa?

Well, that seems alright for a × a × a = aaa. However, lots of things practiced in maths is to convenient/help us.

How about?
a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a × a = aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Wouldn't it be so so so much easier to write a⁷⁹?

Some of the most difficult questions that will come out for your level would look like:
Q9. -2b(-3 + 5b - 8ab²) = 6b - 10b² + 16ab³
Why is it 6b? This is because of -2b × (-3) = +6b.
Why is it -10b²? This is because of -2b × (+5b) = -10b².
Why is it +16ab³? This is because of -2b × (-8ab²) = 16 × b × a × b × b = 16abbb = +16ab³.

Now, do you understand the topic better and have become more confident at how easy maths can be?