Expand and simplify this formula

[Gringo123]

I had to expand and simplify this formula and I got it wrong.
2a + 2 (3a + 2)
I first multiplied the 2a by everything inside the bracket, giving:
6a squared + 4a
Then multiplied the 2 by everything inside the bracket, giving:
6a + 4
so in total I had:
6a squared + 4a + 6a + 4
which I simplified to:
6a squared + 10a + 4

The answer is actually:
8a + 4
Where did I go wrong?

 

[danago]

I had to expand and simplify this formula and I got it wrong.
2a + 2 (3a + 2)
I first multiplied the 2a by everything inside the bracket, giving:
6a squared + 4a
Then multiplied the 2 by everything inside the bracket, giving:
6a + 4
so in total I had:
6a squared + 4a + 6a + 4
which I simplified to:
6a squared + 10a + 4

The answer is actually:
8a + 4
Where did I go wrong?

The problem is in your first step. The bracket is multiplied by just 2, not 2a.

Your method would have been ok if the question was instead (2a + 2) (3a + 2). Note the extra set of brackets? It makes a big difference.

Without the first set of brackets, the expression is essentially saying: "Evaluate '3a+2', multiply this by 2 and then add 2a".
With the first set of brackets, the expression is saying: "Evaluate '3a+2', then evaluate '2a+2', and then multiply these two numbers".

 

[skalaiarasu]

I had to expand and simplify this formula and I got it wrong.
2a + 2 (3a + 2)
I first multiplied the 2a by everything inside the bracket, giving:
6a squared + 4a
Then multiplied the 2 by everything inside the bracket, giving:
6a + 4
so in total I had:
6a squared + 4a + 6a + 4
which I simplified to:
6a squared + 10a + 4

The answer is actually:
8a + 4
Where did I go wrong?

you first multiply the 2 by everything inside the bracket then it will give you correct ...

 

[Gringo123]

Thank a lot Danago!
So as a rule is it true to say that you only multiply everything inside the bracket only by the unit that comes immediately before the bracket? In the case 2?

I got the following 2 questions right, and yet I multiplied everything inside the bracket by everything outside of it. What is the difference?

4(3b - 2) - 5b
ans - 7b -8

6(2c - 1) - 7c
ans - 5c -6

 

[smtcenterchic]

The question you were confused on can be rewritten as 2(3+2a) + 2a, which is the same format as your other problems. See how this is different than what you originally solved, which was (2+2a)(3+2a)?

 

[zzz3293]

kind of, just remember you don't multiply by something you're adding i.e.

3a+a(6-2a)=9a-2a^2
NOT
18a^2-6a^3 do you follow?

 

[Mark44]

Gringo123,
Something that you seem to be struggling with is the order of operations. You might not be aware that some arithmetic operations are more highly privileged than other.

For example, the 2*3 + 5 simplifies to 11. The multiplication takes precedence over the addition, so this is evaluated as 6 + 5 rather that 2*8. The idea of operator precedence also applies to computer programming languages, in case your studies ever take you in that direction.

Back when I was taking algebra years ago, my teach gave us a mnemonic device "My Dear Aunt Sally." The M and D represent multiplication and division; the A and S represent addition and subtraction. The idea is that multiplication or division always take precedence over addition or subtraction.

If you need to change the order of operations, use parentheses () or brackets [] or braces {}.

In your first post, you had 2a + 2 (3a + 2) and got the wrong answer. This is because you misinterpreted the problem as (2a + 2)(3a + 2), which it isn't.

2a + 2 (3a + 2)
= 2a + 6a + 4
= 8a + 4
You have to do the multiplication first - 2 times (3a + 2)
Then you add 2a and the results of the previous step.

 

[zzz3293]

Just to add on a tid bit, Please Excuse My Dear Aunt Sally is a little bit better--Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

 

[Mark44]

When I was learning algebra they hadn't invented exponents or parentheses yet

 

[Mentallic]

When I was learning algebra they hadn't invented exponents or parentheses yet

Except you would've still learned logarithms?

And what about factorizing!?

 

[Mark44]

No, they didn't have them either.

 

[Mentallic]

What an age to be living in...