Lesson: Factoring the Sum and Difference of Two Cubes

In this lesson, we will learn how to factor the sum and the difference of two cubes.

Sample Question Videos

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Worksheet: Factoring the Sum and Difference of Two Cubes • 25 Questions • 4 Videos

Q1:

Given that ๐‘ฅ โˆ’ 5 1 2 = ( ๐‘ฅ โˆ’ 8 ) ๏€น ๐‘ฅ + ๐‘˜ + 6 4 ๏… 3 2 , find an expression for ๐‘˜ .

Q2:

The expression ๐‘ฅ + 2 7 3 has two factors. One factor is ( ๐‘ฅ + 3 ) . What is the other factor?

Q3:

Factorise fully 1 0 0 0 ๐‘ฅ โˆ’ 1 2 5 3 .

Q4:

Factorise fully 6 4 ๐‘ฅ โˆ’ 1 2 5 ๐‘ฆ 3 3 .

Q5:

Factorise fully 5 4 ๐‘ฅ โˆ’ 1 6 ๐‘ฆ 3 3 .

Q6:

Factorise fully ๐‘ฅ โˆ’ 1 8 3 .

Q7:

Factorise fully ๐‘Ž + ๐‘ 2 4 2 7 .

Q8:

Factorise fully ๐‘ฅ + 8 ๐‘ฆ 3 3 .

Q9:

Factorise fully 6 4 ๐‘ฅ โˆ’ 7 2 9 ๐‘ฆ 6 6 .

Q10:

If ๐‘Ž โˆ’ ๐‘ = 4 5 3 3 and ๐‘Ž โˆ’ ๐‘ = 9 , what is the value of ๐‘Ž + ๐‘Ž ๐‘ + ๐‘ 2 2 ?

Q11:

Complete the following: = ( ๐‘ฆ + 1 5 ๐‘ฅ ) ๏€น ๐‘ฆ โˆ’ 1 5 ๐‘ฆ ๐‘ฅ + 2 2 5 ๐‘ฅ ๏… 2 2 .

Q12:

Complete the factorisation: 1 0 0 0 ๐‘ฅ โˆ’ 7 2 9 = ( 1 0 ๐‘ฅ โˆ’ 9 ) ( โ‹ฏ โ‹ฏ โ‹ฏ โ‹ฏ ) 3 .

Q13:

Complete the following: 7 2 9 ๐‘ฅ + 8 = ( + ) ๏€น 8 1 ๐‘ฅ โˆ’ 1 8 ๐‘ฅ + ๏… 3 2 .

Q14:

If ๐‘ฅ โˆ’ ๐‘ฆ = 5 5 2 2 , ๐‘ฅ โˆ’ ๐‘ฆ = โˆ’ 5 , and ๐‘ฅ โˆ’ ๐‘ฅ ๐‘ฆ + ๐‘ฆ = 4 9 2 2 , what is the value of ๐‘ฅ + ๐‘ฆ 3 3 ?

Q15:

What is the result of ๏€น 2 7 ๐‘ฅ โˆ’ 1 ๏… รท ( 3 ๐‘ฅ โˆ’ 1 ) 3 , where 3 ๐‘ฅ โ‰  1 ?

Q16:

Factorise fully ( ๐‘ฅ โˆ’ 6 ๐‘ฆ ) โˆ’ 2 1 6 ๐‘ฆ 3 3 .

Q17:

Factorise fully โˆ’ 1 9 2 ๐‘ฅ ๐‘ฆ โˆ’ 3 7 5 ๐‘ฆ 3 4 .

Q18:

Factorise fully 7 2 9 ๐‘ฅ โˆ’ 3 4 3 3 .

Q19:

If ๐‘ฆ + ๐‘Ž = ( ๐‘ฆ โˆ’ 3 ) ๏€น ๐‘ฆ + 3 ๐‘ฆ + 9 ๏… 3 2 , what is the value of ๐‘Ž ?

Q20:

Factorise fully ( 9 ๐‘ฅ + 7 ๐‘ฆ ) โˆ’ 7 2 9 ๐‘ฅ 3 3 .

Q21:

Factorise fully ( 2 ๐‘ฅ + 7 ๐‘ฆ ) โˆ’ ( 2 ๐‘ฅ โˆ’ 7 ๐‘ฆ ) 3 3 .

Q22:

If ๐‘ฅ + ๐‘˜ = ( ๐‘ฅ + ๐‘˜ ) ๏€น ๐‘ฅ โˆ’ 2 ๐‘ฅ + ๐‘˜ ๏… 3 3 2 2 , what is the value of ๐‘˜ ?

Q23:

Expand and simplify ๏€น ๐‘ฅ โˆ’ 5 ๏… ๏€น ๐‘ฅ + 5 ๏… + 5 2 3 3 , and then factorise the result completely.

Q24:

Factorise fully 1 2 1 6 ๐‘ฅ โˆ’ 1 2 5 ๐‘ฆ 3 3 .

Q25:

Factorise fully ( ๐‘ฅ โˆ’ ๐‘ฆ ) โˆ’ 2 1 6 ( ๐‘ฅ โˆ’ ๐‘ฆ ) 4 .

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