What is the correct factorised form of 9x² − 16 = 0?
Answer and explanation
Correct answer: (3x − 4)(3x + 4) = 0
The governing identity is the difference of two squares: a² − b² = (a − b)(a + b). Rewrite 9x² − 16 as (3x)² − 4². Substituting a = 3x and b = 4 gives (3x − 4)(3x + 4), so the equation becomes (3x − 4)(3x + 4) = 0. Expanding verifies the result: 9x² + 12x − 12x − 16 = 9x² − 16, because the middle terms cancel. Option B expands to an expression containing an incorrect linear term, while option C represents a repeated factor and does not equal the original difference. Option D also gives incorrect coefficients. Hence option A is the correct factorisation.
Frequently asked questions
What is the correct answer to this question?
(3x − 4)(3x + 4) = 0
Why is this the correct answer?
The governing identity is the difference of two squares: a² − b² = (a − b)(a + b). Rewrite 9x² − 16 as (3x)² − 4². Substituting a = 3x and b = 4 gives (3x − 4)(3x + 4), so the equation becomes (3x − 4)(3x + 4) = 0. Expanding verifies the result: 9x² + 12x − 12x − 16 = 9x² − 16, because the middle terms cancel. Option B expands to an expression containing an incorrect linear term, while option C represents a repeated factor and does not equal the original difference. Option D also gives incorrect coefficients. Hence option A is the correct factorisation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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