Expand the Binomial Square: (7+x)(7+x) Step by Step

Q: Why isn't (7+x)² just 49 + x²?

When you square a binomial, you get three terms, not two! The formula is (a+b)² = a² + 2ab + b². You're missing the middle term 2ab, which equals 2(7)(x) = 14x.

Q: How do I remember the binomial square formula?

Think "First squared, plus twice the product, plus last squared". For (7+x)²: 7² + 2(7·x) + x² = 49 + 14x + x².

Q: Can I use FOIL instead of the formula?

Absolutely! FOIL gives the same result: First: 7 × 7 = 49Outer: 7 × x = 7xInner: x × 7 = 7xLast: x × x = x² Combined: 49 + 7x + 7x + x² = 49 + 14x + x²

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

Pick a simple number for x (like x=1) and calculate both (7+x)² and your expanded form. If x=1: (7+1)² = 64, and 49+14(1)+1² = 64 ✓

Binomial Squares with Algebraic Terms

$(7+x)(7+x)=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 Any factor multiplied by itself is actually squared

00:08 Therefore the brackets are squared

00:14 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

$(7+x)(7+x)=\text{?}$

Step-by-step solution

According to the shortened multiplication formula:

Since 7 and X appear twice, we raise both terms to the power:

$(7+x)^2$

Final Answer

$(7+x)^2$

Key Points to Remember

Essential concepts to master this topic

Rule: (a+b)² = a² + 2ab + b² for all binomial squares
Technique: For (7+x)², calculate 7² + 2(7)(x) + x² = 49 + 14x + x²
Check: Expand by FOIL: (7+x)(7+x) = 49 + 7x + 7x + x² = 49 + 14x + x² ✓

Common Mistakes

Avoid these frequent errors

Forgetting the middle term 2ab
Don't just square each term separately: (7+x)² ≠ 49 + x² = missing 14x! This happens when you forget the cross-multiplication terms from FOIL. Always use the complete formula (a+b)² = a² + 2ab + b².

Practice Quiz

Test your knowledge with interactive questions

Choose the expression that has the same value as the following:

$$ (x+3)^2 $$

FAQ

Everything you need to know about this question

Why isn't (7+x)² just 49 + x²?

When you square a binomial, you get three terms, not two! The formula is (a+b)² = a² + 2ab + b². You're missing the middle term 2ab, which equals 2(7)(x) = 14x.

How do I remember the binomial square formula?

Think "First squared, plus twice the product, plus last squared". For (7+x)²: 7² + 2(7·x) + x² = 49 + 14x + x².

Can I use FOIL instead of the formula?

Absolutely! FOIL gives the same result:

First: 7 × 7 = 49
Outer: 7 × x = 7x
Inner: x × 7 = 7x
Last: x × x = x²

Combined: 49 + 7x + 7x + x² = 49 + 14x + x²

What if the binomial has subtraction like (7-x)²?

Use the same formula but watch the signs! (7-x)² = 7² + 2(7)(-x) + (-x)² = 49 - 14x + x². The middle term becomes negative.

How can I check if my expansion is correct?

Pick a simple number for x (like x=1) and calculate both (7+x)² and your expanded form. If x=1: (7+1)² = 64, and 49+14(1)+1² = 64 ✓

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