762 views

### Expand and simplify (5x – 2y)(3x – 4y)

Expand and simplify (5x – 2y)(3x – 4y)

In this question, we are asked to 'expand' out the brackets. What this means is we need each term in one set of brackets (5x and -2y) to be multiplied by each term in the other set of brackets (3x and -4y).

So let's take this step-by-step.

We're going to use a simple technique which will help us in any future questions where we need to expand brackets. This is the FOIL technique:

F = first

O = outside

I  = inside

L = last

1) We start from of FOIL by multiplying together both of our first terms.

These are 5x and 3x because if we look at each bracket separately, these are the two individual terms that come first:

5x*3x = 15x^2

(5 times 3 = 15 and x times x = x^2)

2) Next we use of FOIL by multiplying together the terms on the outside of the brackets.

These are 5x and -4y because when both brackets are side by side, we can see that these terms are on the outer part of the equation.

5x*-4y = -20xy

(5 times -4 = -20 and x times y = xy)

3) Then we use of FOIL by multiplying together the terms on the inside of the brackets.

These are -2y and 3x because when both brackets are side by side, we can see that these terms are on the inner part of the equation.

-2y*3x = -6xy

(-2 times 3 = -6 and x times y = xy)

4) Finally we use L of FOIL by multiplying together the last terms of the brackets.

These are -2y and -4y because if we look at each bracket separately, these are the two individual terms that come last:

-2y*-4y = 8y^2

(-2 times -4 = 8 and y times y = y^2)

5) Now let's look at what terms we're left with after each of those 4 steps using our FOIL technique:

15x^2 - 20xy - 6xy + 8y^2

Our last step is to 'simplify' our answer by collecting any like terms. These are terms which have the same algebraic ending when we ignore the number in front of them.

So in this case, we have xy terms which we can collect: -20xy-6xy = -26xy.

6) Our final answer will be 15x^2 - 26xy + 8y^2.

REMEMBER:

Do check your signs when you look over your answers and your working. It's easy to make silly mistakes when you multiply a negative term with another negative term, for example (the answer will be positive).

1 year ago

Answered by Jamie, a GCSE Maths tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 531 SUBJECT SPECIALISTS

£22 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my years of experience tutoring, we will be able to surpass the grades you want!”

£24 /hr

Sioned D.

Degree: Law (Bachelors) - University College London University

Subjects offered:Maths, History+ 4 more

Maths
History
English
Biology
.LNAT.
-Personal Statements-

“Hello! I'm a University College London Final year Law Student with a great deal of tutoring experience in English, Maths, Sciences and Entrance Exams. ”

Jamie L.

Currently unavailable: for new students

Degree: Civil Engineering (Masters) - Bristol University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Physics
Further Mathematics
Chemistry

“My name is Jamie and I am a 4th year Civil Engineering Student at Bristol University. I also spent my year abroad at McGill University in Canada. I have a real passion for Maths and Science, and love toshare this passion with my stude...”

### You may also like...

#### Other GCSE Maths questions

Can you solve the following 2 simultaneous equations; y=6x-2 and x^2-4x+19=y?

(2x + 3y)^2 – (2x – 3y)^2 = 360 show that xy is a multiple of 5

What is the range of solutions for the inequality 2(3x+1) > 3-4x?

The circle c has equation x^2 + y^2 = 1. The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.