Algebra- Expanding and simplifying equations

Expanding and Simplifying Algebraic Equations

 

Here we are going to take a look at how to expand and simplify Algebraic Equations;

Example 1

 

When multiplying out two brackets make sure that each term in the second bracket is multiplied by each term in the first bracket.

See examples below, I've colour coded the steps of the equations to make them simpler to understand.

 

An easy way to multiply out two brackets is to use the grid method shown below;

Grid method for (x  +  3) ( x  +  4)

 

Example 2

 

Again multiply all the terms in the second bracket by the terms in the first bracket

 

 

The grid method for (2x  -  4) (x  -  5)

 

Example 3

 

Again we'll multiply all the terms in the second bracket by the terms in the first bracket;

 

In this equation (4x-  3) ( 3x  +  1)

 as there are no like terms to gather we just write out the expanded expression;

 

12x3  +  4x2  -  9x  -  3

 

 The grid method for (4x-  3) (3x  +  1)

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Comments 18 comments

carolina muscle profile image

carolina muscle 6 years ago from Charlotte, North Carolina

You make this seem a lot simpler !!! Thanks!


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Thankyou for your positive comment carolina muscle, it makes the effort to show the workings out of maths worthwhile.


BkCreative profile image

BkCreative 6 years ago from Brooklyn, New York City

Good grief - this is soooo clear! I tutor students sometimes and there is absolutely nothing clear that I can show them when it comes to simplifying - until now. Wow! So of course I can bookmark and use this. Whew! The colors, the arrows, it all helps tremendously.

Oh, I never got around to writing about the golden ratio - but maybe I will now because it is a shape we are so familiar with - like our credit cards, and driver licenses and so much more. Glad you mentioned that.

Great to find clear math - whew!

Rated up and more.


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Thanks Bk Creative... I find that I have achieved what I set out to do in this tutorial via your comments. My daughter has dyslexia and dyspraxia, as a result I found writing in black didn't achieve anything so I used this principle, I found that it helped immensely especially when colour coded and written out in steps form.

She is now at Uni doing a degree in Sport Science and this year they have given her a reader for her exams.

Prior due to lack of funding she didn't receive any help other than my own.

My daughters classmates found this method extremely helpful as well because they could visually see the process they had to follow to attain the answer.

Many thanks for your wonderful comments.

Looking forward to reading your hub on the "golden ratio"


secret 6 years ago

Im learning this in school but my sums are like this

5x(x-2)?

=7x? i don't know? helllp


t.elia profile image

t.elia 6 years ago from Northern Ireland Author

Hi secret.

Thankyou for being brave enough to write in.

At the moment in school you are learning to expand the brackets, therefore

5x (x - 2 )

5x multiplied by x = 5x^2

5x multiplied by -2 = -10x

= 5x^2 - 10x (this is the answer)

5x squared - 10x


meee 5 years ago

what do all these letters mean?!?


Jelly 5 years ago

Wow! This helped me a lot, thanks for making it seem so simplse! :)


helpppp 5 years ago

p^2(2p-1)


t.elia profile image

t.elia 5 years ago from Northern Ireland Author

HELPPP

You are multiplying out the brackets here;

p^2(2p - 1)

p^2 x p = p^3 ( to multiply these you add them)

Then multiply out your 2

and finally do the last part of this equation;

p^2 x 1 = p^2

The answer now looks like this

2p^3 - p^2 (Ans)

Good Luck


academysigma profile image

academysigma 4 years ago from Hong Kong

Hi T.Elia - thanks for this, I've linked to this hub from one of mine, I hope you're ok with that. If not, pls. let me know.


t.elia profile image

t.elia 4 years ago from Northern Ireland Author

Academysigma,

Thanks that is no problem glad you found it useful.

Telia


Cazza 4 years ago

I need to work out 9xy(5x+6y)I have no idea what to do can you help me and fast please. Thanks


t.elia profile image

t.elia 4 years ago from Northern Ireland Author

Hi Cazza

9xy(5x + 6y)

9 x 5 = 45

X x X = X^2

y

+

9 x 6 = 54

X

Y x Y = Y^2

Regroup this as 45X^2Y + 54XY^2 (Ans)

Hope this helps


nice 4 years ago

(X-3/2Y)^5 pls! expand. thank you


unknown 4 years ago

how do i simplify and expand 2(x+5)(x-2)


Step 4 years ago

I need to find an equation that relates to 1 & 2, 2 & 8, 3 & 18, and 4 & 32


t.elia profile image

t.elia 3 years ago from Northern Ireland Author

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