What is the expanded form of the polynomial \(3x(2x^2-5x+4)\)?
Answer and explanation
Correct answer: \(6x^3-15x^2+12x\)
Using the distributive law, multiply \(3x\) by each term inside the parentheses: \(3x\cdot2x^2=6x^3\), \(3x\cdot(-5x)=-15x^2\), and \(3x\cdot4=12x\). Therefore, the expanded form is \(6x^3-15x^2+12x\). Option B fails to multiply each term by \(x\), while option D has the wrong sign for the middle term. Exam tip: when removing parentheses, multiply the outside term by every term inside and use \(x^m\cdot x^n=x^{m+n}\) for powers.
Frequently asked questions
What is the correct answer to this question?
\(6x^3-15x^2+12x\)
Why is this the correct answer?
Using the distributive law, multiply \(3x\) by each term inside the parentheses: \(3x\cdot2x^2=6x^3\), \(3x\cdot(-5x)=-15x^2\), and \(3x\cdot4=12x\). Therefore, the expanded form is \(6x^3-15x^2+12x\). Option B fails to multiply each term by \(x\), while option D has the wrong sign for the middle term. Exam tip: when removing parentheses, multiply the outside term by every term inside and use \(x^m\cdot x^n=x^{m+n}\) for powers.
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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