Expand (7+b)(a+9): Step-by-Step Binomial Multiplication

Q: Why do I get four terms instead of two?

When multiplying two binomials, you must multiply every term in the first by every term in the second. Since each binomial has 2 terms, you get 2×2 = 4 products total!

Q: What order should I write the final answer?

Write terms in standard form: highest degree first. So $ ab + 7a + 9b + 63 $ is correct because ab has degree 2, while 7a and 9b have degree 1, and 63 has degree 0.

Q: Can I combine any of these terms?

No! The terms ab, 7a, 9b, and 63 are all unlike terms - they have different variables or powers. Unlike terms cannot be combined or simplified further.

Q: Is there a shortcut for this multiplication?

The FOIL method IS the shortcut! Remember: First, Outer, Inner, Last. This systematic approach ensures you don't miss any of the four required products.

Q: What if I get the terms in different order?

The order doesn't affect correctness, but standard form (highest degree first) is preferred. As long as you have all four terms: ab, 7a, 9b, and 63, you're right!

Q: How do I check my multiplication is correct?

Count terms: Should have exactly 4 termsCheck degrees: One degree-2 term (ab), two degree-1 terms (7a, 9b), one constant (63)Verify coefficients: 7×9=63, other coefficients match original

Binomial Multiplication with Mixed Variables

$(7+b)(a+9)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

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

00:20 Calculate the products

00:43 Arrange the expression

00:53 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

$(7+b)(a+9)=$

Step-by-step solution

To solve this problem, we'll use the distributive property, also known as the FOIL method when dealing with two binomials.

Let's expand the expression $(7+b)(a+9)$ :

First, apply the distributive property by multiplying each term in the first binomial by each term in the second binomial. This means we will have four operations:
Step 1: Multiply $7$ by $a$ . This gives $7a$ .
Step 2: Multiply $7$ by $9$ . This gives $63$ .
Step 3: Multiply $b$ by $a$ . This gives $ab$ .
Step 4: Multiply $b$ by $9$ . This gives $9b$ .

After performing these operations, the expression expands to:

$7a + 63 + ab + 9b$

Rearrange the terms in standard form for the final answer, which is:

$ab + 7a + 9b + 63$

Therefore, the solution to the problem is $ab + 7a + 9b + 63$ .

Final Answer

$ab+7a+9b+63$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: Multiply First, Outer, Inner, Last terms systematically
Technique: (7+b)(a+9) = 7·a + 7·9 + b·a + b·9
Check: Expand back: ab + 7a + 9b + 63 has four distinct terms ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply all four term combinations
Don't just multiply 7×a and b×9 = 7a + 9b! This misses two crucial products and gives an incomplete answer. Always multiply each term in the first binomial by each term in the second binomial to get all four products.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I get four terms instead of two?

When multiplying two binomials, you must multiply every term in the first by every term in the second. Since each binomial has 2 terms, you get 2×2 = 4 products total!

What order should I write the final answer?

Write terms in standard form: highest degree first. So $ab + 7a + 9b + 63$ is correct because ab has degree 2, while 7a and 9b have degree 1, and 63 has degree 0.

Can I combine any of these terms?

No! The terms ab, 7a, 9b, and 63 are all unlike terms - they have different variables or powers. Unlike terms cannot be combined or simplified further.

Is there a shortcut for this multiplication?

The FOIL method IS the shortcut! Remember: First, Outer, Inner, Last. This systematic approach ensures you don't miss any of the four required products.

What if I get the terms in different order?

The order doesn't affect correctness, but standard form (highest degree first) is preferred. As long as you have all four terms: ab, 7a, 9b, and 63, you're right!

How do I check my multiplication is correct?

Count terms: Should have exactly 4 terms
Check degrees: One degree-2 term (ab), two degree-1 terms (7a, 9b), one constant (63)
Verify coefficients: 7×9=63, other coefficients match original

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