What is the expansion of \(4x(3x^2-2x+5)\)?
Answer and explanation
Correct answer: \(12x^3-8x^2+20x\)
Using the distributive law, multiply \(4x\) by every term in the bracket: \(4x\cdot3x^2=12x^3\), \(4x\cdot(-2x)=-8x^2\), and \(4x\cdot5=20x\). Therefore, the expansion is \(12x^3-8x^2+20x\). Option B fails to multiply each term by the outside factor \(4x\). Exam tip: when multiplying a monomial by a polynomial, distribute it to every term and combine the powers of the same variable.
Frequently asked questions
What is the correct answer to this question?
\(12x^3-8x^2+20x\)
Why is this the correct answer?
Using the distributive law, multiply \(4x\) by every term in the bracket: \(4x\cdot3x^2=12x^3\), \(4x\cdot(-2x)=-8x^2\), and \(4x\cdot5=20x\). Therefore, the expansion is \(12x^3-8x^2+20x\). Option B fails to multiply each term by the outside factor \(4x\). Exam tip: when multiplying a monomial by a polynomial, distribute it to every term and combine the powers of the same variable.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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