What is ( a^3-b^3 ) equal to?
Answer and explanation
Correct answer: ( (a-b)(a^2+ab+b^2) )
The difference of cubes identity is \\(a^3-b^3=(a-b)(a^2+ab+b^2)\\). Applying it directly gives \\(a^3-b^3=(a-b)(a^2+ab+b^2)\\). Multiplying the factors confirms the result: the terms combine to \\(a^3-ab^2+a^2b+ab^2-b^3=a^3-b^3\\).
Therefore, option A is correct. The factor outside the bracket has a minus sign, while all three terms inside the second factor have positive signs. Option B is the identity for a sum of cubes, not a difference. Option C is the cube of a difference and contains different middle terms, while option D concerns squares rather than cubes. Keeping the degree and signs distinct avoids confusion.
Frequently asked questions
What is the correct answer to this question?
( (a-b)(a^2+ab+b^2) )
Why is this the correct answer?
The difference of cubes identity is \\(a^3-b^3=(a-b)(a^2+ab+b^2)\\). Applying it directly gives \\(a^3-b^3=(a-b)(a^2+ab+b^2)\\). Multiplying the factors confirms the result: the terms combine to \\(a^3-ab^2+a^2b+ab^2-b^3=a^3-b^3\\).
Therefore, option A is correct. The factor outside the bracket has a minus sign, while all three terms inside the second factor have positive signs. Option B is the identity for a sum of cubes, not a difference. Option C is the cube of a difference and contains different middle terms, while option D concerns squares rather than cubes. Keeping the degree and signs distinct avoids confusion.
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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