Topic Details (Notes format)

How to Factor the Difference of Squares

Subject: Mathematics

Book: Maths Mastery

A difference of squares takes the form a² – b² and factors into (a – b)(a + b). For example, x² – 9 becomes (x – 3)(x + 3). This factoring pattern simplifies advanced algebraic expressions, helps solve polynomial equations quickly, and appears often in geometry proofs or optimization tasks. Recognizing a² – b² is crucial in polynomial manipulation, partial fraction decomposition, and problem-solving across arithmetic, geometry, and calculus contexts, making it a powerful tool in your algebraic toolkit.

Practice Questions

What is the square root of 144?

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If a number is divisible by 9, it is also divisible by which of the following?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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If 8x = 512, what is the value of x?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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A sphere has a radius of 7 cm. What is its volume?

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What is the remainder when 5^100 is divided by 3?

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What is the sum of all even numbers between 1 and 50?

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