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In this lesson, we will learn how to multiply the sum of two terms with their difference to get the polynomial known as βthe difference of two squares.β

Q1:

Expand the product ( π₯ + 1 ) ( π₯ β 1 ) .

Q2:

Use the difference of two squares identity to expand ( 3 π + 7 ) ( 3 π β 7 ) .

Q3:

If π₯ β π = ( π₯ + 5 ) ( π₯ β 5 ) 2 , what is the value of π ?

Q4:

Expand the product ( 2 π + π ) ( 2 π β π ) .

Q5:

If π₯ β π¦ = 9 and π₯ + π¦ = 1 0 , what is the value of π₯ β π¦ 2 2 ?

Q6:

Complete the following: π₯ β = ( π₯ β 5 ) ( π₯ + 5 ) 2 .

Q7:

If π₯ + π¦ = 2 and π₯ β π¦ = 6 , what is the value of π₯ β π¦ 2 2 ?

Q8:

If π₯ + π β 2 5 = ( π₯ + 5 ) ( π₯ β 5 ) 2 , what is the value of π ?

Q9:

Given that π + π = 5 and π β π = 4 5 2 2 , find π β π .

Q10:

If π β π = 6 4 2 2 and π + π = 4 , what is the value of π β π ?

Q11:

What is the value of ο» β 7 + β 3 ο ο» β 7 β β 3 ο 3 3 ?

Q12:

Simplify ( 4 π§ + 7 ) ( 4 π§ β 7 ) .

Q13:

Given that π₯ = 2 and π¦ = β 3 , find the value of 3 ( π₯ + π¦ ) ( π₯ β π¦ ) 4 4 .

Q14:

Given that π₯ β π¦ = 6 2 2 2 and π₯ β π¦ = β 3 1 , find π₯ + π¦ .

Q15:

Given that π₯ = 5 β 7 β β 2 and π¦ = β 7 β β 2 , find π₯ β π¦ 2 2 expressing your answer in simplest form.

Q16:

Expand ( 2 π₯ β 3 ) ( 2 π₯ + 3 ) .

Q17:

Simplify ο» β 3 + 2 ο ο» β 3 β 2 ο .

Q18:

What is the area of a rectangle of length ( π₯ + 1 4 ) cm and width ( π₯ β 1 4 ) cm?

Q19:

If π₯ β π = ( π₯ + 1 0 ) ( π₯ β 1 0 ) 2 , what is the value of π ?

Q20:

If π β π = 1 0 and π + π = 1 8 , what is the value of π β π 2 2 ?

Q21:

If π β π = 5 and π + π = 1 4 , what is the value of π β π 2 2 ?

Q22:

If π₯ + π¦ = 9 and π₯ β π¦ = 6 , what is the value of π₯ β π¦ 2 2 ?

Q23:

Given that π₯ + π§ = 3 and π₯ β π§ = 3 2 2 , find π₯ β π§ .

Q24:

If π₯ + π β 1 4 4 = ( π₯ + 1 2 ) ( π₯ β 1 2 ) 2 , what is the value of π ?

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