Expand and Simplify: 2(x+3)² + 3(x+2)² Expression

Q: Do I square the 2 in front of the parentheses?

No! The coefficient stays outside. First expand $ (x+3)^2 = x^2+6x+9 $, then multiply everything by 2 to get $ 2x^2+12x+18 $.

Q: What's the difference between (2x+3)² and 2(x+3)²?

$ (2x+3)^2 $ means you square the entire expression 2x+3. But $ 2(x+3)^2 $ means you square x+3 first, then multiply by 2. They give completely different results!

Q: How do I expand (x+3)² without making mistakes?

Use the pattern: $ (x+a)^2 = x^2 + 2ax + a^2 $. For $ (x+3)^2 $: first term is $ x^2 $, middle term is $ 2(x)(3) = 6x $, last term is $ 3^2 = 9 $.

Q: Why do I get different answers when I combine like terms?

Make sure you're combining correctly: $ 2x^2 + 3x^2 = 5x^2 $ (not 6x²), and $ 12x + 12x = 24x $ (not 12x). Write out each step clearly!

Q: Can I use FOIL to expand the squares?

Yes! $ (x+3)^2 = (x+3)(x+3) $, then FOIL: First: x·x = x²Outer: x·3 = 3xInner: 3·x = 3xLast: 3·3 = 9 Result: $ x^2 + 3x + 3x + 9 = x^2 + 6x + 9 $

Perfect Square Expansion with Coefficient Multiplication

$2(x+3)^2+3(x+2)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 We'll use the shortened multiplication formulas to open the parentheses

00:38 We'll solve the squares and products

00:59 We'll properly open parentheses and multiply by each factor

01:29 We'll collect like terms

01:44 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

$2(x+3)^2+3(x+2)^2=$

Step-by-step solution

In order to solve the exercise, remember the abbreviated multiplication formulas:

$(x+y)^2=x^2+2xy+y^2$

Let's start by using the property in both cases:

$(x+3)^2=x^2+6x+9$

$(x+2)^2=x^2+4x+4$

We then reinsert them back into the formula as follows:

$2(x^2+6x+9)+3(x^2+4x+4)=$

$2x^2+12x+18+3x^2+12x+12=$

$5x^2+24x+30$

Final Answer

$5x^2+24x+30$

Key Points to Remember

Essential concepts to master this topic

Formula: Use $(x+a)^2 = x^2 + 2ax + a^2$ to expand squares
Technique: Distribute coefficients after expanding: $2(x^2+6x+9) = 2x^2+12x+18$
Check: Combine like terms carefully: $2x^2+3x^2=5x^2$ and $12x+12x=24x$ ✓

Common Mistakes

Avoid these frequent errors

Squaring the coefficient along with the binomial
Don't write $2(x+3)^2$ as $(2x+6)^2$ = wrong expansion! This squares the 2 instead of keeping it as a multiplier. Always expand $(x+3)^2$ first, then multiply by 2.

Practice Quiz

Test your knowledge with interactive questions

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

$$ (x+y)^2 $$

FAQ

Everything you need to know about this question

Do I square the 2 in front of the parentheses?

No! The coefficient stays outside. First expand $(x+3)^2 = x^2+6x+9$ , then multiply everything by 2 to get $2x^2+12x+18$ .

What's the difference between (2x+3)² and 2(x+3)²?

$(2x+3)^2$ means you square the entire expression 2x+3. But $2(x+3)^2$ means you square x+3 first, then multiply by 2. They give completely different results!

How do I expand (x+3)² without making mistakes?

Use the pattern: $(x+a)^2 = x^2 + 2ax + a^2$ . For $(x+3)^2$ : first term is $x^2$ , middle term is $2(x)(3) = 6x$ , last term is $3^2 = 9$ .

Why do I get different answers when I combine like terms?

Make sure you're combining correctly: $2x^2 + 3x^2 = 5x^2$ (not 6x²), and $12x + 12x = 24x$ (not 12x). Write out each step clearly!

Can I use FOIL to expand the squares?

Yes! $(x+3)^2 = (x+3)(x+3)$ , then FOIL:

First: x·x = x²
Outer: x·3 = 3x
Inner: 3·x = 3x
Last: 3·3 = 9

Result:

x^2 + 3x + 3x + 9 = x^2 + 6x + 9

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