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Multiply out and simplify - OCR - GCSE Maths - Question 17 - 2023 - Paper 1

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Multiply out and simplify. (3x + y)(x + 2y)

Worked Solution & Example Answer:Multiply out and simplify - OCR - GCSE Maths - Question 17 - 2023 - Paper 1

Step 1

Multiply out

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Answer

To multiply the two binomials, we use the distributive property (FOIL method):

  1. First: Multiply the first terms of each binomial:
    3ximesx=3x23x imes x = 3x^2.

  2. Outer: Multiply the outer terms:
    3ximes2y=6xy3x imes 2y = 6xy.

  3. Inner: Multiply the inner terms:
    yimesx=xyy imes x = xy.

  4. Last: Multiply the last terms:
    yimes2y=2y2y imes 2y = 2y^2.

Combining these results gives:

3x2+6xy+xy+2y23x^2 + 6xy + xy + 2y^2

Step 2

Simplify

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Answer

Now, combine like terms:

The terms 6xy6xy and xyxy are like terms, so we add them: 6xy+xy=7xy6xy + xy = 7xy

Thus, the expression simplifies to: 3x2+7xy+2y23x^2 + 7xy + 2y^2

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