What is the correct factorisation of (125p^3-8q^3)?
Answer and explanation
Correct answer: ( (5p-2q)(25p^2+10pq+4q^2) )
The expression is a difference of two cubes because \\(125p^3=(5p)^3\\) and \\(8q^3=(2q)^3\\). The identity for a difference of cubes is \\(a^3-b^3=(a-b)(a^2+ab+b^2)\\). Substituting \\(a=5p\\) and \\(b=2q\\) gives \\((5p-2q)(25p^2+10pq+4q^2)\\).
Thus option A is correct. The second factor contains a plus sign between all three terms; this is a key feature of the difference-of-cubes identity. Option B uses the corresponding sum-of-cubes pattern, while C uses incorrect cube roots and D treats the whole expression as the cube of a binomial. Expansion of option A returns the original expression.
Frequently asked questions
What is the correct answer to this question?
( (5p-2q)(25p^2+10pq+4q^2) )
Why is this the correct answer?
The expression is a difference of two cubes because \\(125p^3=(5p)^3\\) and \\(8q^3=(2q)^3\\). The identity for a difference of cubes is \\(a^3-b^3=(a-b)(a^2+ab+b^2)\\). Substituting \\(a=5p\\) and \\(b=2q\\) gives \\((5p-2q)(25p^2+10pq+4q^2)\\).
Thus option A is correct. The second factor contains a plus sign between all three terms; this is a key feature of the difference-of-cubes identity. Option B uses the corresponding sum-of-cubes pattern, while C uses incorrect cube roots and D treats the whole expression as the cube of a binomial. Expansion of option A returns the original expression.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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