Find the Error A student multiplied 6.5xy(4x2+8y2).

Question

Identify the student's error. 6.5xy(4x2+8y2)=26x2y+52xy2


Multiple choice question.
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A)
The student multiplied instead of adding the exponents.

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B)
The student added instead of multiplying the exponents.

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C)
The student multiplied instead of dividing the exponents.

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D)
The student divided instead of subtracting the exponents.

Answer 1

The student's error can be identified by looking at how they expanded the expression \( 6.5xy(4x^2 + 8y^2) \).

To correctly multiply, we distribute \( 6.5xy \) to each term inside the parentheses:

1. Multiply \( 6.5xy \) by \( 4x^2 \): \[ 6.5xy \cdot 4x^2 = 26x^{1+2}y = 26x^3y \]

2. Multiply \( 6.5xy \) by \( 8y^2 \): \[ 6.5xy \cdot 8y^2 = 52xy^{1+2} = 52xy^3 \]

Thus, the correct expansion is: \[ 26x^3y + 52xy^3 \]

The error in the student's original calculation was that they applied incorrect exponent rules when they wrote \( 26x^2y + 52xy^2 \).

Based on the provided multiple-choice options, the most fitting choice is:

A) The student multiplied instead of adding the exponents.

This reflects the error in handling the exponent during the multiplication process.