**Introduction**

Do you struggle with expanding algebraic linear expressions during your Math examinations?

Keep on reading for a step-by-step guide to expanding linear expressions, along with some useful tips to make the topic of Algebra easier for you!

**Let’s Take A Look At This Algebra Question**

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## Let’s Solve Part (A)

First, let us copy the question.

💡

What Do The Brackets Mean?💡It means that you are supposed to multiply the number outside the brackets to everything inside the brackets

Therefore, we are going to multiply 2 to -4x and +3.

Some of you may know this method as the **Distributive Law**. Some may know this as the **Rainbow Method** because the arrows look like a rainbow 🌈

🌈

How To Remember The Distributive Law In Algebra🌈Think of a rainbow! 🌈

Do you panic just by looking at the algebraic expression above? Don’t worry because I am going to share a trick I have been teaching my students.

Look inside the brackets and ask yourself how many terms there are in the equation.

There are two terms inside the bracket. These are -4*x* and +3.

To help you visualise and differentiate the two terms, you can draw a line between the two.

Now, you can start multiplying by drawing arrows 🌈

The arrow 🌈 below signifies multiplication. So let us multiply 2 with -4*x*.

That is -8x.

Let us move on to the next term and do the same. Draw an arrow 🌈 and multiply 2 by +3.

The answer is +6.

Therefore, our final answer is -8*x* + 6.

## Answer For Part (A)

**-8 x + 6**

## Let’s Solve Part (B)

Again, the brackets mean we need to multiply 3*x* with all of the terms inside the brackets.

How many terms are inside the brackets? There are two! Let us draw a line to separate the two terms.

Next, draw your arrow 🌈 and multiply.

3*x* x *x*

**= 3 x^{2}**

When you are multiplying *x* with *x*, you will get *x*^{2}.

If this does not make sense to you, remember that when you are multiplying 11 by 11 in index notation, you will get 11^{2}. So the same is true when *x* is multiplied by *x*.

Next, let us multiply 3x with +5 🌈

We will get 15*x*.

Therefore, our final answer is 3*x*^{2} + 15*x.*

## Answer For Part (B)

**3 x^{2} + 15x**

## Let’s Solve Part (C)

Apply the same steps that we did in the previous equations. Let us determine the terms that we have inside the bracket.

We have 2*x* and -5.

Next, let us multiply 🌈 them with the number outside the bracket.

-7 x 2*x*

=-14*x*

For the second term, what is -7 x -5? 🌈

😲

What HappensWhen You Multiply Two NegativeNumbers?😲A negative and a negative make a positive.

Therefore, it is +35.

Our final answer is -14*x* + 35.

## Answer For Part (C)

**-14x + 35**

## Let’s Solve Part (D)

For some of you, this last algebraic equation might seem strange because there is only a minus sign and no number outside the bracket.

🚀

Remember This WhenYou See A Negative Sign Outside The Bracket🚀Whenever you see algebraic equations like this, remember that there is a hidden 1 and the minus sign represents -1. You can write down 1 after the negative sign so you won’t get confused!

Now, we can proceed with the next steps. Draw a line between the two terms inside the bracket.

Next, multiply 🌈 the number outside the bracket with the first term.

-1 x 7*x*

= -7*x*

Next, draw an arrow 🌈 and multiply -1 with -1.

-1 x -1 = +1

Therefore, the answer is -7*x* + 1.

🤔

Remember This Shortcut When Multiplying Against A Negative Sign🤔The negative sign outside will flip all the signs inside the bracket.

Inside the brackets, I have a +7*x* and -1. When the brackets are removed, the minus sign will flip the signs of the terms in the bracket.

Therefore, it will be -7*x* + 1.

## Answer For Part (D)

**-7x + 1**

## Conclusion

Looking at algebraic expressions can be overwhelming when you do not know where to start but I hope that this Algebra blog post has served as your guide in understanding how to expand linear expressions.

Remember to draw a line between the terms inside the bracket before multiplying each term so you won’t get confused.

Stay tuned for more blog posts about Algebra!

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