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

To simplify the expression, we will use the distributive property (also known as the FOIL method for binomials).

1. Distribute 3x:

   • Multiply 3x by each term in the second binomial:
     • $3x \cdot x = 3x^2$
     • $3x \cdot 2y = 6xy$

2. Distribute y:

   • Multiply y by each term in the second binomial:
     • $y \cdot x = xy$
     • $y \cdot 2y = 2y^2$

3. Combine all the terms:

   • Now, we combine all the results: $3x^2 + 6xy + xy + 2y^2$
   • Combine like terms (specifically, the xy terms): $3x^2 + (6xy + xy) + 2y^2 = 3x^2 + 7xy + 2y^2$

Thus, the simplified expression is: $3x^2 + 7xy + 2y^2$