Expand (2[x+3])²: Solving a Double Bracket Square Expression

Q: Why can't I just square each term separately?

Because (a+b)² ≠ a² + b²! You're missing the middle term 2ab. The correct formula is $ (a+b)^2 = a^2 + 2ab + b^2 $, which gives you three terms, not two.

Q: Do I need to expand the inner brackets first?

Yes! Always work from the inside out. First expand 2[x+3] = 2x+6, then square the result. This makes the problem much clearer and prevents errors.

Q: How do I remember the perfect square formula?

Think "First, twice, last": square the first term, add twice the product of both terms, then square the last term. Practice with simple examples like $ (x+3)^2 $.

Q: What if I get confused about the middle term coefficient?

The middle term is always 2ab where a and b are your two terms. In (2x+6)², that's 2 × 2x × 6 = 24x. Double-check by multiplying the terms and doubling the result!

Q: Can I use FOIL instead of the formula?

Absolutely! FOIL works perfectly: (2x+6)(2x+6) = First + Outer + Inner + Last = 4x² + 12x + 12x + 36 = 4x² + 24x + 36. Both methods give the same answer.

Bracket Expansion with Perfect Square Formula

$(2\lbrack x+3\rbrack)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 Let's open parentheses properly, multiply by each factor

00:15 We'll use shortened multiplication formulas to open the parentheses

00:40 We'll solve the squares and multiplications

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

$(2\lbrack x+3\rbrack)^2=$

Step-by-step solution

We will first solve the exercise by opening the inner brackets:

(2[x+3])²

(2x+6)²

We will then use the shortcut multiplication formula:

(X+Y)²=X²+2XY+Y²

(2x+6)² = 2x² + 2x*6*2 + 6² = 2x+24x+36

Final Answer

$4x^2+24x+36$

Key Points to Remember

Essential concepts to master this topic

Order: First expand inner brackets, then apply square formula
Formula: $(a+b)^2 = a^2 + 2ab + b^2$ where a=2x, b=6
Check: Expand step by step: (2x+6)² = 4x² + 24x + 36 ✓

Common Mistakes

Avoid these frequent errors

Squaring terms individually instead of using the formula
Don't square (2x+6)² as (2x)² + (6)² = 4x² + 36! This misses the middle term 2ab and gives the wrong answer. Always use the complete formula (a+b)² = a² + 2ab + b² to get all three terms.

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 can't I just square each term separately?

Because (a+b)² ≠ a² + b²! You're missing the middle term 2ab. The correct formula is $(a+b)^2 = a^2 + 2ab + b^2$ , which gives you three terms, not two.

Do I need to expand the inner brackets first?

Yes! Always work from the inside out. First expand 2[x+3] = 2x+6, then square the result. This makes the problem much clearer and prevents errors.

How do I remember the perfect square formula?

Think "First, twice, last": square the first term, add twice the product of both terms, then square the last term. Practice with simple examples like $(x+3)^2$ .

What if I get confused about the middle term coefficient?

The middle term is always 2ab where a and b are your two terms. In (2x+6)², that's 2 × 2x × 6 = 24x. Double-check by multiplying the terms and doubling the result!

Can I use FOIL instead of the formula?

Absolutely! FOIL works perfectly: (2x+6)(2x+6) = First + Outer + Inner + Last = 4x² + 12x + 12x + 36 = 4x² + 24x + 36. Both methods give the same answer.

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