1. ## Expanding Expressions Qustions

Hi guys not sure how to approach these questions would appreciate being pointed in the right direction

Question:

Expand the following expressions, collecting together like terms where possible;

1. (ax + b) ^2

2. 4(x/2 - 3 ) (7y - x)

2. 1. To square an expression means to multiply that expression by itself. So this is equal to (ax+b)(ax+b). Can you FOIL this expression?

2. Leave the 4 outside, and FOIL the two binomials. Give it a shot and let's see how you do.

3. Originally Posted by DrSteve
1. To square an expression means to multiply that expression by itself. So this is equal to (ax+b)(ax+b). Can you FOIL this expression?

2. Leave the 4 outside, and FOIL the two binomials. Give it a shot and let's see how you do.
Thanks for the quick response Steve

I'm not familliar with the term FOIL are you possibly refering to multiplying the brackets out?

Thanks

4. Originally Posted by komodo
Thanks for the quick response Steve

I'm not familliar with the term FOIL are you possibly refering to multiplying the brackets out?

Thanks
Yes. FOIL is a mnemonic i think it's called. Multiplying the brackets out is the same thing as expanding an expression, so do that.

5. I think I understand that I have multiply the First, Outter, Inner and Last in that order then collect like terms hence FOIL.

Can someone give me the answers so I can check if I've done it correctly

Thanks guys

6. Originally Posted by komodo
I think I understand that I have multiply the First, Outter, Inner and Last in that order then collect like terms hence FOIL.

Can someone give me the answers so I can check if I've done it correctly

Thanks guys

7. Originally Posted by Quacky
This is what I got for the 1st one not sure if I've done it correctly though....

(ax + b) ^2

= (ax + b) (ax + b)

= (2ax + axb) (axb + b^2)

= 2ax + 2axb + b^2

Is this correct feels like I've done something wrong

8. Originally Posted by komodo
This is what I got for the 1st one not sure if I've done it correctly though....

(ax + b) ^2

= (ax + b) (ax + b)

= (2ax + axb) (axb + b^2)

= 2ax + 2axb + b^2

Is this correct feels like I've done something wrong
Just some silly errors. If I have $\displaystyle ax\times ax$ then this is $\displaystyle a\times a\times x\times x$ (because the order of multiplication doesn't matter) which is the same as $\displaystyle a^2x^2$ So this is the change you need to make:

$\displaystyle a^2x^2 + axb + axb + b^2$ (don't use brackets for addition!)

$\displaystyle =a^2x^2+2axb+b^2$

Otherwise, it's fine. Be careful with how you set your work out, try and follow my example above for the second problem, and just be cautious where you put brackets (implying multiplication) and plus signs (obviously for addition).

9. Originally Posted by Quacky
Just some silly errors. If I have $\displaystyle ax\times ax$ then this is $\displaystyle a\times a\times x\times x$ (because the order of multiplication doesn't matter) which is the same as $\displaystyle a^2x^2$ So this is the change you need to make:

$\displaystyle a^2x^2 + axb + axb + b^2$ (don't use brackets for addition!)

$\displaystyle =a^2x^2+2axb+b^2$
Thanks for the advice it was a pretty stupid mistake....the 2nd expression is also proving kind of tricky its different to all the previous exercises that I've attempted prior but here is a long shot at it:

4 (x/2 - 3) (7y - x)

= 4 (x/2.7y - x^2/2 - 21y - 3x)

Dont know whether to multiply everything in the brackets by the 4 outside or even if whats in the brackets is correct...help would be much appreciated

10. Originally Posted by komodo
Thanks for the advice it was a pretty stupid mistake....the 2nd expression is also proving kind of tricky its different to all the previous exercises that I've attempted prior but here is a long shot at it:

4 (x/2 - 3) (7y - x)

= 4 (x/2.7y - x^2/2 - 21y - 3x)

Dont know whether to multiply everything in the brackets by the 4 outside or even if whats in the brackets is correct...help would be much appreciated
Yeah, you want to multiply everything inside by 4. You've made a slight sign error:

= 4 (x/2.7y - x^2/2 - 21y + 3x) Remember that two negatives make a positive!

Finish up by multiplying through by four.

11. Originally Posted by Quacky
Yeah, you want to multiply everything inside by 4. You've made a slight sign error:

= 4 (x/2.7y - x^2/2 - 21y + 3x) Remember that two negatives make a positive!

Finish up by multiplying through by four.
In that case I have :

4x/2.7y - 4x^2/2 - 84y + 12x (Personaly I cant see any like terms to collect)

Is this more like it?

12. Originally Posted by komodo
In that case I have :

4x/2.7y - 4x^2/2 - 84y + 12x (Personaly I cant see any like terms to collect)

Is this more like it?
Some of your terms are a mess. Remember that multiplication/division are (generally) commutative, meaning they can be done in any order. Your first term there is $\displaystyle \frac{4\times 7 \times x\times y}{2}$ which can be simplified to just $\displaystyle 14xy$

Similarly, $\displaystyle \frac{4x^2}{2}=2x^2$

13. Originally Posted by Quacky
Some of your terms are a mess. Remember that multiplication/division are (generally) commutative, meaning they can be done in any order. Your first term there is $\displaystyle \frac{4\times 7 \times x\times y}{2}$ which can be simplified to just $\displaystyle 14xy$

Similarly, $\displaystyle \frac{4x^2}{2}=2x^2$
Now its starting to make sence wasn't aware that I could do that....therefore I should end up with:

14xy - 2x^2 - 84y + 12x

14. Originally Posted by komodo
Now its starting to make sence wasn't aware that I could do that....therefore I should end up with:

14xy - 2x^2 - 84y + 12x
There we go .

15. Originally Posted by Quacky
There we go .
Thats right lol.......I'm loosing sleep over this stuff

Anyway thanks for help realy appreciate it