Expansion - With Free Algebra Worksheets - The Answer

Hi folks,

Welcome back. I hope you have done the previous algebra worksheets.

If you have not, click here to get the notes and the questions.

Here are the answers and step-by-step working to the previous algebra worksheets:

Expand the following
1. 3(2+x)

= 3×2 + 3.x

= 6 + 3x

2. 4(p+1)

= 4.p + 4×1

= 4p + 4

3. p(3+x)

= p×3 + p.x

= 3p + px

4. 5(2x+1)

= 5×2x + 5×1

= 10x + 5

5. 2(x+y)

= 2×x + 2×y

= 2x + 2y

6. 8(a+2b)

= 8×a + 8×2b

= 8a + 16b

7. ½(2x+4y)

= ½×2x + ½×4y

= x + 2y

8. 8(7c-5d)

= 8×7c + 8×5d

= 56c + 40d

9. 4(-2f+5d)

= 4(-2f) + 4(5d)

= -8f + 20d

10. 6(-m-3n)

= 6(-m) + 6(-3n)

= -6m -18n

more questions

I hope you do enjoy the algebra worksheets. If you have any suggestion, comments and questions, please feel free to comment it.

Expansion - With Free Algebra Worksheets

Hi folks,

Welcome back. Sorry that I did not update this blog for a while. I was actually busy with something else.

Today, we'll be learning about expansion pf some algebra equations.

Expansion

General equation

p(q + r) = pq + pr

For example:
2(x + 3)
= 2.x + 2.3 ( the dots represent multiplication )
= 2x + 6

Here's another example:

3x(y+5)
= 3x.y + 3x.5 ( the dots represent multiplication )
= 3xy + 15x

I think this is pretty straight forward for you folks. If you still don't understand, please don't hesitate to post your question or doubt in the comment column.

Here are some free algebra worksheets on expansion for you.

Expand the following
1. 3(2+x)
2. 4(p+1)
3. p(3+x)
4. 5(2x+1)
5. 2(x+y)
6. 8(a+2b)
7. ½(2x+4y)
8. 8(7c-5d)
9. 4(-2f+5d)
10. 6(-m-3n)

more questions

I will post the answer in the next post. Stay tune!

Speak soon.

Raymond Chua

Answer and solution to Algebra Worksheets #1

Welcome back to Algebra Worksheets.

Here’s the answer to the previous algebra worksheets.

If x = -3 and y = 2, what is the value of the expression 2X² – 5xy?

2X² – 5xy

= 2(-3)² – 5(-3)(2)

= 18 – (-30)

= 18 + 30

= 48

If a = 4 and b = 7, calculate the value of 7a³ + 3ab – 3a².

7a³ + 3ab – 3a²

= 7(4)³ + 3(4)(7) – 3(4)²

= 7(64) + 3(28) – 3(16)

= 448 + 84 – 48

= 580

Given p = 4 and q = 9. Find the value of 4p²q³ – 6p³ + 10q² – 5.

4p²q³ – 6p³ + 10q² – 5

= 4(4)²(9)³ – 6(4)³ + 10(9)² – 5

= 4(16)(729) – 6(64) + 10(81) – 5

= 4(11664) – 384 + 810 – 5

= 46656 – 384 + 810 – 5

= 47077

In Kids Birthday Cake Restaurant, 3 cheese cakes and 2 swiss rolls cost $22.40. But 4 cheese cakes and 3 swiss rolls cost $31.20. Calculate the price of a cheese cake and a swiss roll.

Let cheese cake = x

Let swiss roll = y

3x + 2y = $22.40 ---- 1

4x + 3y = $31.20 ---- 2

Multiply the equation 1 with 3

(3x + 2y = $22.40) ×3 and you will get

9x + 6y = $67.20 ---- 3

Multiply equation 2 with 2

(4x + 3y = $31.20) × 2 and you’ll get

8x + 6y = $62.40 ---- 4

Equation 3 – equation 4:

9x + 6y = $67.20 ---- 3

8x + 6y = $62.40 ---- 4

---------------------------

X = $5.20

Substitute x = $5.20 into equation 1

3x + 2y = $22.40

3($5.20) + 2y = $22.40

$15.60 + 2y = $22.40

2y = $22.40 - $15.60

2y = $6.80

y = $6.80/2

y = $3.40

Answer: A cheese cake cost $5.20 and a swiss roll cost $3.40

What? Still hungry for more algebra worksheets? Go to the comment section and tell me how hungry you are.

Free Algebra Worksheets #1

Are you ready for the first edition of my free algebra worksheets?

Here it goes:

1. If x = -3 and y = 2, what is the value of the expression 2X² – 5xy?

2. If a = 4 and b = 7, calculate the value of 7a³ + 3ab – 3a².

3. Given p = 4 and q = 9. Find the value of 4p²q³ – 6p³ + 10q² -5

4. In Kids Birthday Cake Restaurant, 3 cheese cakes and 2 swiss rolls cost $22.40. But 4 cheese cakes and 3 swiss rolls cost $31.20. Calculate the price of a cheese cake and a swiss roll.

Get more algebra worksheets here

As usual, please post your comment in the comment column. Thanks

I will update the answer for this algebra question in the coming post. So, please bookmark this page or subscribe to the rss to make sure that you remember to come later to check for your answer for this free algebra worksheets.

Speak soon

Raymond Chua

The Answer for the Previous Algebra Worksheets

Hi folks, welcome back to Algebra Worksheets.

If you haven't read the previous post, which is the question, I suggest you to read it first. Click here.

Answer:

Let's count the number of tank which can be filled the those 4 taps in an hour first.

The first tap can fill up 1 tank in an hour.

The second tap can fill up 4/3 tank per hour. (1/3 tank per quarter hour)

The third tap can fill up 2 tanks in an hour.

The fourth tap can fill up 4 tanks per hour.


So, if all the taps were turned on at the same time, they are capable to fill up

(1+4/3+2+4) tanks = 8 + 1/3 tank = 25/3 tank


If

1 hour = 25/3 tank

then

1 tank will be equivalent to 3/25hour

1 tank = 3/25 hour
= (3/25 X 60) minutes
= 7.2 minutes
= 7 minutes and 12 seconds.

more Algebra Worksheets

If you still not clear with the solution, please comment and let me know your problem.

Good luck and Happy Learning!

Watch out for more Algebra Worksheets in the coming post.


Raymond Chua

Tickle Your Brain With This Algebra Worksheet

Hi folks, are you ready to give your brain some exercise? If you do, try this simple Algebra Worksheets.

Here's the question:

You have a tank which has 4 taps. The first tap can fill the tank in an hour. The second tap can fill the tank in 45 minutes. The third tap can fill the tank in 30 minutes and the fourth tap can fill up the tank in just 15 minutes.

Now, my question is, how long will it take to fill up the whole tank if all the four taps are all turned on at the same time?

Please post your answer in the comment section. Feel free to include the working if you can.

I'll get this back to you.

Good luck!


Raymond Chua
P.S. I will provide more algebra worksheets in the future. That will depend on how many comments there are to motivate me. :)

Algebra Worksheets - Introduction

Hi folks,

I am a mathematics lovers and I have a very strong passion towards Mathematics. In fact, it is one of my favorite subjects. In this blog, I will focus on Algebra Worksheets and Tutorial. :)

If I have a decent amount of visitors, I may consider to include other topics such as linear equation, trigonometri, geometrical construction, functions, pythagoras' theorem and others.

From now on, I will provide you with Algebra tutorial and Algebra Worksheets.

Speak soon.

Raymond Chua