Write a × b using algebraic notation.

Recall the convention: a × b Write the letters together: a × b = ab State the answer: ab Answer: ab

Write 3 × y using algebraic notation.

Recall the convention: 3 × y Write the number in front: 3 × y = 3y State the answer: 3y Answer: 3y

Write 5 × n without a multiplication sign.

Recall the convention: 5 × n Combine: 5 × n = 5n State the answer: 5n Answer: 5n

Write a × a using index notation.

Spot the repeated letter: a × a Use a power: a × a = a^2 State the answer: a^2 Answer: a^2

Write a × a × a using index notation.

Count the copies: a × a × a Use a power: a × a × a = a^3 State the answer: a^3 Answer: a^3

Algebraic notation Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Algebraic notation questions. See exactly how to solve problems on writing products, dropping the times sign, coefficients, powers.

writing productsdropping the times signcoefficientspowersindex notationalphabetical order

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Write

a \times b

using algebraic notation.

Worked solution

Recall the convention
$a \times b$
In algebra we do not write the multiplication sign between letters.
Write the letters together
$a \times b = ab$
Placing the letters side by side means 'a times b'.
State the answer
ab
So a × b is written ab.

Answer

Question 2

1 markeasy

Write

3 \times y

using algebraic notation.

Worked solution

Recall the convention
$3 \times y$
A number multiplied by a letter is written with the number first and no times sign.
Write the number in front
$3 \times y = 3y$
The 3 is the coefficient of y.
State the answer
$3y$
So 3 × y is written 3y.

Answer

3y

Question 3

1 markeasy

Write

5 \times n

without a multiplication sign.

Worked solution

Recall the convention
$5 \times n$
The number is written before the letter with no sign between them.
Combine
$5 \times n = 5n$
5n means 'five lots of n'.
State the answer
$5n$
So 5 × n is written 5n.

Answer

5n

Question 4

1 markeasy

Write

a \times a

using index notation.

Worked solution

Spot the repeated letter
$a \times a$
The same letter is multiplied by itself.
Use a power
$a \times a = a^2$
Two copies multiplied is written as a squared.
State the answer
$a^2$
So a × a is written a².

Answer

a^2

Question 5

1 markeasy

Write

a \times a \times a

using index notation.

Worked solution

Count the copies
$a \times a \times a$
The letter a is multiplied by itself three times.
Use a power
$a \times a \times a = a^3$
Three copies multiplied is a cubed.
State the answer
$a^3$
So a × a × a is written a³.

Answer

a^3

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