2.3.4 Difference of two squares

The difference of two squares is when a squared number is subtracted from another squared number.

e.g.

\( x^2-y^2, 6^2-2^2 \)

To factorize the difference of two squares

• Use the identity \( a^2-b^2=(a+b)(a-b) \)

Worked example:

Factorise completely.

\( y^2-9x^2 \)

As both terms are squared terms and the second is subtracted from first, so we can factorize using the square of two terms rewrite the expression

\( y^2-9x^2=y^2-(3x)^2 \)

By using the identity \( a^2-b^2=(a+b)(a-b) \)

\( y^2-(3x)^2=(y-3x)(y+3x) \)

\( (y-3x)(y+3x) \)

Test yourself

Question 1:

Factorise completely.

\( 3a^2b-ab^2 \)

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Question 2:

Expand and simplify.

\( (x+7)(x-3) \)

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Question 3:

Factorise

\( 24+5x-x^2 \)

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Question 4:

Factorise completely.

\( 81k^2-m^2 \)

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Question 5:

Write \( (x+1)(x-3)^2 \) in the form \( ax^3+bx^2+cx+d\).

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Question 6:

Factorise

\( 12ab^3+18a^3b^2 \)

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