MYTUTOR SUBJECT ANSWERS

1981 views

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 F 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).

Maymana A. 11 Plus Maths tutor, GCSE Maths tutor, GCSE Chemistry tuto...

1 year ago

Answered by Maymana, a GCSE Maths tutor with MyTutor


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

461 SUBJECT SPECIALISTS

£20 /hr

Sam F.

Degree: Economics with Placement (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Extended Project Qualification
Economics

“Studying for BSc Hons Economics, A level economics, maths and physics. Able to tutor GCSE/AS/A2 Economics, Maths and GCSE physics! ”

£18 /hr

Sahil N.

Degree: Medicine (Bachelors) - Queen Mary, London ('13) University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“About me: Hi there! I'm Sahil, a friendly and enthusiastic medical student at Barts and the London School of Medicine. Teaching has always been a wonderful passion of mine and I truly believe there is nothing more satisfying than help...”

£30 /hr

Michelangelo M.

Degree: MMath Mathematics with Placement (Masters) - Bath University

Subjects offered:Maths, Italian+ 4 more

Maths
Italian
Further Mathematics
Computing
.STEP.
.MAT.

“Mathematics student at the University of Bath, willing to help you love this subject and improve your grades.”

About the author

£18 /hr

Maymana A.

Degree: Natural Sciences (Masters) - University College London University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Expand (2x-3)(4x+4) using the FOIL method.

Rationalise 1/(√7) ?

The functions f and g are defined on R , the set of real numbers by f(x) = x^2 - 5x +2, and g(x) = 1 - x. Find h(x) = f(g(x)), and j(x) = g(f(x)).

How do you solve simultaneous equations?

View GCSE Maths tutors

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

mtw:mercury1:status:ok