Expand (x+m)(3/4+5x): Step-by-Step Binomial Multiplication

Binomial Multiplication with Mixed Terms

(x+m)(34+5x)=? (x+m)(\frac{3}{4}+5x)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the expression
00:03 Open parentheses properly, multiply each factor by each factor
00:28 Calculate the products
00:39 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

(x+m)(34+5x)=? (x+m)(\frac{3}{4}+5x)=\text{?}

2

Step-by-step solution

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

  • Step 1: Apply the distributive property to expand the expression.

  • Step 2: Perform the multiplication for each pair of terms.

  • Step 3: Combine any like terms.

Now, let's work through each step:
Step 1: We have the expression (x+m)(34+5x)(x + m)(\frac{3}{4} + 5x). We'll distribute each term in the first binomial across each term in the second binomial.
Step 2: The expression expands by distributing as follows: x(34)+x(5x)+m(34)+m(5x) x(\frac{3}{4}) + x(5x) + m(\frac{3}{4}) + m(5x) .
Step 3: Perform the multiplications: 34x+5x2+34m+5mx\frac{3}{4}x + 5x^2 + \frac{3}{4}m + 5mx.

Note that there are no like terms to combine further.

Therefore, the solution to the problem is 34x+5x2+34m+5mx \frac{3}{4}x + 5x^2 + \frac{3}{4}m + 5mx .

3

Final Answer

34x+5x2+34m+5mx \frac{3}{4}x+5x^2+\frac{3}{4}m+5mx

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Multiply each term in first binomial by each term in second
  • FOIL Method: x34=34x x \cdot \frac{3}{4} = \frac{3}{4}x and x5x=5x2 x \cdot 5x = 5x^2
  • Final Check: Count four terms in expanded form: two with x, one with x2 x^2 , one with m ✓

Common Mistakes

Avoid these frequent errors
  • Adding terms instead of multiplying
    Don't add (x+m)+(34+5x)=x+m+34+5x (x+m) + (\frac{3}{4}+5x) = x + m + \frac{3}{4} + 5x ! This completely ignores the multiplication between binomials. Always distribute each term from the first binomial to every term in the second binomial.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

\( 3+3+3+3 \)

\( 3\times4 \)

FAQ

Everything you need to know about this question

Why do I get four terms in my answer?

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When you multiply two binomials, you get four terms because each term in the first binomial multiplies each term in the second. That's 2 × 2 = 4 terms total!

How do I handle the fraction 34 \frac{3}{4} ?

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Treat the fraction just like any other number! When you multiply x×34 x \times \frac{3}{4} , you get 34x \frac{3}{4}x . The variable goes next to the fraction.

Should I combine 34x \frac{3}{4}x and 5mx 5mx ?

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No! These are not like terms because one has variable x and the other has variables mx. Only combine terms with exactly the same variables and exponents.

What if I mess up the order of my terms?

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The order doesn't matter in addition! 34x+5x2+34m+5mx \frac{3}{4}x + 5x^2 + \frac{3}{4}m + 5mx is the same as 5x2+34x+5mx+34m 5x^2 + \frac{3}{4}x + 5mx + \frac{3}{4}m .

How can I check if my expansion is correct?

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Try substituting simple values like x = 1 and m = 1 into both the original expression and your answer. If they give the same result, you're correct!

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