Algebra: How To Expand Linear Expressions

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

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 -4x 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 -4x.

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 -8x + 6.

Answer For Part (A)

-8x + 6

Let’s Solve Part (B)

Again, the brackets mean we need to multiply 3x 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.

3x x x

= 3x²

When you are multiplying x with x, you will get x².

If this does not make sense to you, remember that when you are multiplying 11 by 11 in index notation, you will get 11². So the same is true when x is multiplied by x.

Next, let us multiply 3x with +5 🌈

We will get 15x.

Therefore, our final answer is 3x² + 15x.

Answer For Part (B)

3x² + 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 2x and -5.

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

-7 x 2x

=-14x

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

😲 What Happens When You Multiply Two Negative Numbers? 😲

A negative and a negative make a positive.

Therefore, it is +35.

Our final answer is -14x + 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 When You 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 7x

= -7x

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

-1 x -1 = +1

Therefore, the answer is -7x + 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 +7x and -1. When the brackets are removed, the minus sign will flip the signs of the terms in the bracket.

Therefore, it will be -7x + 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!