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

Q: How do I keep track of all the signs when expanding?

Write out each multiplication step! For $ (2x+9)(y-4) $, show: 2x·y = +2xy, 2x·(-4) = -8x, 9·y = +9y, 9·(-4) = -36.

Q: Why do some expressions have the same xy term but different results?

The $ 2xy $ term comes from multiplying the variable terms together. The differences are in the linear terms (like 8x vs 8y) and constants, which depend on the specific binomial factors.

Q: What's the fastest way to expand binomials?

Use FOIL: First terms, Outer terms, Inner terms, Last terms. For $ (2x+9)(y+4) $: F=2xy, O=8x, I=9y, L=36, giving $ 2xy + 8x + 9y + 36 $.

Q: How can I check if my expansion is correct?

Count your terms! You should get exactly 4 terms after expanding. Also, substitute simple values like x=1, y=1 into both the original and expanded forms - they should give the same result.

Q: Why does (2x+9)(y+4) give 8x but (2y+9)(x+4) gives 8y?

The coefficient 8 comes from 2 × 4 = 8. In the first case, it's attached to x because you're multiplying 2x by 4. In the second case, it's attached to y because you're multiplying 2y by 4.

Binomial Expansion with Sign Variation

Join expressions of equal value

$(2x+9)(y+4)$
$(2y+9)(x+4)$
$(2x-9)(y-4)$
$(2x+9)(y-4)$
a. $2xy+8x+9y+36$
b. $2xy-8x+9y-36$
c. $2xy-8x-9y+36$
d. $2xy+8y+9x+36$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Open parentheses

00:04 Open parentheses properly, multiply each factor by each factor

00:12 Calculate the products and collect terms

00:16 This is the simplification to 1, we'll use the same method for each expression

00:59 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Join expressions of equal value

$(2x+9)(y+4)$
$(2y+9)(x+4)$
$(2x-9)(y-4)$
$(2x+9)(y-4)$
a. $2xy+8x+9y+36$
b. $2xy-8x+9y-36$
c. $2xy-8x-9y+36$
d. $2xy+8y+9x+36$

Step-by-step solution

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.

Final Answer

4-b, 3-c, 2-d, 1-a

Key Points to Remember

Essential concepts to master this topic

FOIL Method: Multiply First, Outer, Inner, Last terms systematically
Technique: For (2x+9)(y-4), get 2xy - 8x + 9y - 36
Check: Count terms and verify signs match the original binomials ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative signs during multiplication
Don't forget that (+9)(-4) = -36, not +36! Missing negative signs creates completely wrong expanded forms. Always track each sign carefully: positive × negative = negative, negative × negative = positive.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

How do I keep track of all the signs when expanding?

Write out each multiplication step! For $(2x+9)(y-4)$ , show: 2x·y = +2xy, 2x·(-4) = -8x, 9·y = +9y, 9·(-4) = -36.

Why do some expressions have the same xy term but different results?

The $2xy$ term comes from multiplying the variable terms together. The differences are in the linear terms (like 8x vs 8y) and constants, which depend on the specific binomial factors.

What's the fastest way to expand binomials?

Use FOIL: First terms, Outer terms, Inner terms, Last terms. For $(2x+9)(y+4)$ : F=2xy, O=8x, I=9y, L=36, giving $2xy + 8x + 9y + 36$ .

How can I check if my expansion is correct?

Count your terms! You should get exactly 4 terms after expanding. Also, substitute simple values like x=1, y=1 into both the original and expanded forms - they should give the same result.

Why does (2x+9)(y+4) give 8x but (2y+9)(x+4) gives 8y?

The coefficient 8 comes from 2 × 4 = 8. In the first case, it's attached to x because you're multiplying 2x by 4. In the second case, it's attached to y because you're multiplying 2y by 4.

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