How to simplify and expand (distributive property help)?

[breasal]

I keep getting bad grades in math because I don't get the distributive property. I know it's supposed to be a(b + c) = ab + ac but when I try to apply it it doesn't work. I tried expanding 4a + 8b into 2(4b+a) and 5a + 10b into 2(5a+b) but they were both wrong.

I did it like that because for 9m+3n, the correct answer was 3(3m+n). So for 4a + 8b, 2*4 = 8 so I thought 2(4b+a) would work because it would give me 8b+2a... even though that's not right.. I just don't know.

I've read dozens of explanations, but when the problem doesn't look like the example, I get lost. Can you please explain the basic rule of what to do in the simplest language possible?

[caelin]

I keep getting bad grades in math because I don't get the distributive property. I know it's supposed to be a(b + c) = ab + ac but when I try to apply it it doesn't work. I tried expanding 4a + 8b into 2(4b+a) and 5a + 10b into 2(5a+b) but they were both wrong.

I did it like that because for 9m+3n, the correct answer was 3(3m+n). So for 4a + 8b, 2*4 = 8 so I thought 2(4b+a) would work because it would give me 8b+2a... even though that's not right.. I just don't know.

I've read dozens of explanations, but when the problem doesn't look like the example, I get lost. Can you please explain the basic rule of what to do in the simplest language possible?

"I tried expanding 4a + 8b into 2(4b+a) and 5a + 10b into 2(5a+b) but they were both wrong."

You need to factor out the highest number that both coefficients are divisible by.

For 4a + 8b, both the 4 and the 8 are evenly divisible by 4. Factor out the 4 to get 4(a + 2b).

When you multiply that back out, the 4 multiplies by 'a' giving you 4a and the 4 multiplies by 2b giving you 8b.

For 5a + 10b, both 5 and 10 are divisible by 5. Factor out the 5 to get 5(a + 2b).

When you multiply that back out, the 5 multiplies by 'a' giving you 5a and the 5 multiplies by 2b giving you 10b.

[reuben29]

Even if you don't get the highest common factor on your first try, you can still factor the expression again:

For 4a + 8b, use 2 firs to get:

4a + 8b = 2(2a + 4b)

Since 2a and 4b are both divisible by 2, do it again:

2(2a + 4b) = 2 * 2(a + 2b) or 4(a + 2b)

[atworth49]

What you did was not expanding, but factoring (the inverse of expanding)

To factor, find greatest common factor, factor it out, then divide everything inside parentheses by that factor:

4a + 8b ----> GCF = 4
= 4 (4a/4 + 8b/4)
= 4 (a + 2b)

To check, expand it and you get 4a + 8b ----> ok

5a + 10b ----> GCF = 5
= 5 (5a/5 + 10b/5)
= 5 (a + 2b)

9m + 3n ----> GCF = 3
= 3 (9m/3 + 3n/3)
= 3 (3m + n)

Don't rely on other examples to solve, just divide everything by common factor

[darik]

to simplify 4a + 8b, divide by 4 to get 4(a + 2b).

to simplify 5a + 10b, divide by 5 to get 5(a + 2b).

the same for 9m + 3n. divide by 3 to get 3(3m + n).

stay on this same thought for all similar problems.