Solve (X+4)(3+X) Given X=4: Binomial Multiplication Problem

Binomial Multiplication with Variable Substitution

Solve the exercise below given that:X=4 X=4

(X+4)(3+X) (X+4)(3+X)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's tackle this math problem together!
00:13 First, we'll substitute X with 4, based on the given data. Let's solve it step by step.
00:27 Next, calculate each part inside the parentheses separately.
00:32 Remember, there's multiplication between these parentheses.
00:36 And there you have it, that's our solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the exercise below given that:X=4 X=4

(X+4)(3+X) (X+4)(3+X)

2

Step-by-step solution

We start by substituting the value of X X

(4+4)(3+4) (4+4)(3+4)

First, we perform the calculation in parentheses

(8)(7) (8)(7)

After this, we solve the parentheses and can continue with the simple multiplication exercise.

7×8=56 7\times 8=56

3

Final Answer

56

Key Points to Remember

Essential concepts to master this topic
  • Substitution Rule: Replace variable with given value before any calculations
  • Technique: Simplify parentheses first: (4+4)(3+4) becomes (8)(7)
  • Check: Substitute X=4 into original: (4+4)(3+4) = 8×7 = 56 ✓

Common Mistakes

Avoid these frequent errors
  • Expanding binomials before substituting the variable
    Don't expand (X+4)(3+X) to X²+7X+12 then substitute = extra work and error risk! This makes the problem unnecessarily complex. Always substitute the given value first, then simplify the arithmetic.

Practice Quiz

Test your knowledge with interactive questions

\( 9+3-1= \)

FAQ

Everything you need to know about this question

Should I expand the binomials first or substitute X=4 first?

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Always substitute first! When you're given a specific value for the variable, replace it immediately. This turns algebra into simple arithmetic: (X+4)(3+X) (X+4)(3+X) becomes (8)(7)=56 (8)(7) = 56 .

What if I accidentally expanded the binomials first?

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No problem! If you get X2+7X+12 X^2 + 7X + 12 , just substitute X=4: 42+7(4)+12=16+28+12=56 4^2 + 7(4) + 12 = 16 + 28 + 12 = 56 . You'll get the same answer, but it's more work.

Why do I get the wrong answer when I don't use parentheses?

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Without parentheses, you might calculate 4+4×3+4 = 4+12+4 = 20 instead of (4+4)×(3+4) = 8×7 = 56. Always keep the grouping when substituting!

How can I check my answer is correct?

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Substitute X=4 back into the original expression and verify: (4+4)(3+4)=8×7=56 (4+4)(3+4) = 8×7 = 56 . If your calculation gives the same result, you're correct!

Does the order of multiplication matter?

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No! (8)(7) (8)(7) gives the same result as (7)(8) (7)(8) because multiplication is commutative. Both equal 56.

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