Match Equivalent Expressions: Solving (2x+9)(y+4) and Related Binomials

To solve the problem, we'll follow these steps:

• Step 1: Expand each factored expression using the distributive property.
• Step 2: Match the expanded expressions with their corresponding forms.

Step 1: Expand the factored expressions:

- $(2x+9)(y+4)$:
Apply the distributive property:
$(2x)y + (2x)4 + 9y + 36 = 2xy + 8x + 9y + 36$.

- $(2y+9)(x+4)$:
Apply the distributive property:
$(2y)x + (2y)4 + 9x + 36 = 2xy + 8y + 9x + 36$.

- $(2x-9)(y-4)$:
Apply the distributive property:
$(2x)y - (2x)4 - 9y + 36 = 2xy - 8x - 9y + 36$.

- $(2x+9)(y-4)$:
Apply the distributive property:
$(2x)y - (2x)4 + 9y - 36 = 2xy - 8x + 9y - 36$.

Step 2: Match the expanded forms to their corresponding choices:

• 4-b: $(2x+9)(y-4) = 2xy - 8x + 9y - 36$
• 3-c: $(2x-9)(y-4) = 2xy - 8x - 9y + 36$
• 2-d: $(2y+9)(x+4) = 2xy + 8y + 9x + 36$
• 1-a: $(2x+9)(y+4) = 2xy + 8x + 9y + 36$

Therefore, the correct matching of expressions is 4-b, 3-c, 2-d, 1-a.