Match Equivalent Expressions: (12x-5)(y+2) and Related Binomials

Q: How do I remember which terms to multiply together?

Use the FOIL method: First, Outer, Inner, Last. For $ (12x-5)(y+2) $, multiply: 12x·y, 12x·2, (-5)·y, (-5)·2.

Q: Why do I keep getting the signs wrong?

Remember that the sign is part of the term! When you see (12x-5), think of it as (12x + (-5)). This helps you correctly multiply (-5) × 2 = -10, not +10.

Q: What if my expanded expression doesn't match any of the answer choices?

Double-check your distribution first! Make sure you multiplied all four combinations. Then verify your arithmetic - especially signs and coefficients.

Q: Can I combine like terms after expanding?

Yes, but only if there are actually like terms! In this problem, terms like 12xy, 24x, -5y, and -10 are all different, so they cannot be combined.

Q: Is there a pattern to matching these expressions?

Focus on the coefficients and signs after expansion. Each binomial product creates a unique combination of terms that matches exactly one expanded form in the answer choices.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Open parentheses

00:05 We will use the shortened multiplication formulas to open the parentheses

00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Match together expressions of equal value

$(12x-5)(y+2)$
$(x-12)(5y+2)$
$(12x+5)(y-2)$
a. $12xy-24x+5y-10$
b. $12xy+24x-5y-10$
c. $5xy+2x-60y-24$

2

Step-by-step solution

Let's simplify the given expressions, open the parentheses using the extended distribution law:

$(\textcolor{red}{a}+\textcolor{blue}{b})(c+d)=\textcolor{red}{a}c+\textcolor{red}{a}d+\textcolor{blue}{b}c+\textcolor{blue}{b}d$

In the formula template for the above distribution law, we take by default that the operation between the terms inside of the parentheses is addition. Note that the sign preceding the term is an inseparable part of it. Furthermore we will apply the laws of sign multiplication to our expression. We will then open the parentheses using the above formula, where there is an addition operation between all terms.

Proceed to simplify each of the expressions in the given problem, whilst making sure to open the parentheses using the mentioned distribution law, the commutative law of addition and multiplication and combining like terms (if there are like terms in the expression obtained after opening the parentheses):

$(12x-5)(y+2) \\ \downarrow\\ \big(12x+(-5)\big)(y+2)\\ 12x\cdot y+12x\cdot 2+(-5)\cdot y+(-5)\cdot 2\\ \boxed{12xy+24x-5y-10}\\$
$(x-12)(5y+2) \\ \downarrow\\ \big(x+(-12)\big)(5y+2)\\ x\cdot 5y+x\cdot 2+(-12)\cdot 5y+(-12)\cdot 2\\ \boxed{5xy+2x-60y-24}\\$
$(12x+5)(y-2) \\ \downarrow\\ (12x+5)\big(y+(-2)\big)\\ 12x\cdot y+12x\cdot (-2)+5\cdot y+5\cdot (-2)\\\ \boxed{12xy-24x+5y-10}\\$
Note in all expressions where we performed the multiplication between the expressions in the parentheses above, the result of the multiplication (obtained after applying the aforementioned distribution law) yielded an expression where terms cannot be combined. Due to the fact that all terms in the resulting expression are different from each other (remember that all variables in like terms need to be identical and have the same exponent),
After applying the commutative law of addition and multiplication we observe that:
The simplified expression in 1 matches the expression in option B,
The simplified expression in 2 matches the expression in option C,
The simplified expression in 3 matches the expression in option A,

Therefore, the correct answer (among the suggested options) is answer B.

3

Final Answer

1-c, 2-b, 3-a

Key Points to Remember

Essential concepts to master this topic

Distribution Law: Multiply each term by each term systematically
Technique: $(12x-5)(y+2) = 12xy + 24x - 5y - 10$
Check: Count four terms after expansion and verify signs ✓

Common Mistakes

Avoid these frequent errors

Missing terms when expanding binomials
Don't just multiply the first terms or forget some combinations = incomplete expansion! Students often get (12x-5)(y+2) = 12xy - 5y instead of all four terms. Always multiply EVERY term in the first binomial by EVERY term in the second binomial.

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 remember which terms to multiply together?

+

Use the FOIL method: First, Outer, Inner, Last. For $(12x-5)(y+2)$ , multiply: 12x·y, 12x·2, (-5)·y, (-5)·2.

Why do I keep getting the signs wrong?

+

Remember that the sign is part of the term! When you see (12x-5), think of it as (12x + (-5)). This helps you correctly multiply (-5) × 2 = -10, not +10.

What if my expanded expression doesn't match any of the answer choices?

+

Double-check your distribution first! Make sure you multiplied all four combinations. Then verify your arithmetic - especially signs and coefficients.

Can I combine like terms after expanding?

+

Yes, but only if there are actually like terms! In this problem, terms like 12xy, 24x, -5y, and -10 are all different, so they cannot be combined.

Is there a pattern to matching these expressions?

+

Focus on the coefficients and signs after expansion. Each binomial product creates a unique combination of terms that matches exactly one expanded form in the answer choices.

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Match Equivalent Expressions: (12x-5)(y+2) and Related Binomials

Binomial Multiplication with Distribution Law

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