Solve (3x+4)(x+2)=3x²+2 Using the Distributive Property

Q: What does 'distributive property' mean exactly?

The distributive property means $ a(b + c) = ab + ac $. For $ (3x+4)(x+2) $, you multiply each term in the first parentheses by each term in the second parentheses.

Q: Why do I get four terms when expanding?

You get four terms because you multiply 2 terms × 2 terms = 4 products: $ 3x \cdot x $, $ 3x \cdot 2 $, $ 4 \cdot x $, and $ 4 \cdot 2 $. Then combine like terms!

Q: How do I know which terms to combine?

Like terms have the same variable part. In $ 3x^2 + 6x + 4x + 8 $, combine $ 6x + 4x = 10x $ because both have just x. The $ 3x^2 $ and 8 stay separate.

Q: What if the x² terms don't cancel out?

If the $ x^2 $ terms don't cancel, you'd have a quadratic equation instead of linear. In this problem, both sides have $ 3x^2 $, so they subtract to zero, leaving a simple linear equation.

Q: Can I solve this without expanding first?

You must expand the left side to see what you're working with! Without expanding $ (3x+4)(x+2) $, you can't compare it properly to $ 3x^2 + 2 $ on the right side.

Polynomial Expansion with Equation Solving

Solve the equation using the distributive property:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

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

00:34 Calculate the multiplications

00:47 Simplify what's possible

01:04 Collect like terms

01:14 Isolate X

01:30 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

Solve the equation using the distributive property:

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

Step-by-step solution

To solve the equation $(3x+4)(x+2) = 3x^2 + 2$ , we start by expanding the left-hand side using the distributive property.

First, distribute each component of the first polynomial:

$(3x+4)(x+2) = 3x(x+2) + 4(x+2)$

Next, distribute inside each term:

$3x(x+2) = 3x \cdot x + 3x \cdot 2 = 3x^2 + 6x$ $4(x+2) = 4 \cdot x + 4 \cdot 2 = 4x + 8$

Combining these, we have:

$3x^2 + 6x + 4x + 8 = 3x^2 + 10x + 8$

Set the expanded expression equal to the right side of the original equation:

$3x^2 + 10x + 8 = 3x^2 + 2$

To solve for $x$ , subtract $3x^2$ from both sides:

$10x + 8 = 2$

Next, subtract 8 from both sides to isolate the term involving $x$ :

$10x = 2 - 8$

$10x = -6$

Finally, divide both sides by 10:

$x = \frac{-6}{10}$ $x = -0.6$

Therefore, the solution to the equation is $-0.6$ .

The correct choice from the provided options is $\boxed{-0.6}$ .

Final Answer

$-0.6$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply each term by every term in parentheses
Technique: $3x(x+2) = 3x^2 + 6x$ and $4(x+2) = 4x + 8$
Verification: Substitute $x = -0.6$ back: both sides equal $0.28$ ✓

Common Mistakes

Avoid these frequent errors

Not distributing to all terms completely
Don't just multiply $3x \cdot x = 3x^2$ and forget the rest = missing crucial terms! This leaves out $6x + 4x + 8$ terms that change the entire equation. Always distribute each term in the first polynomial to every term in the second polynomial.

Practice Quiz

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

FAQ

Everything you need to know about this question

What does 'distributive property' mean exactly?

The distributive property means $a(b + c) = ab + ac$ . For $(3x+4)(x+2)$ , you multiply each term in the first parentheses by each term in the second parentheses.

Why do I get four terms when expanding?

You get four terms because you multiply 2 terms × 2 terms = 4 products: $3x \cdot x$ , $3x \cdot 2$ , $4 \cdot x$ , and $4 \cdot 2$ . Then combine like terms!

How do I know which terms to combine?

Like terms have the same variable part. In $3x^2 + 6x + 4x + 8$ , combine $6x + 4x = 10x$ because both have just x. The $3x^2$ and 8 stay separate.

What if the x² terms don't cancel out?

If the $x^2$ terms don't cancel, you'd have a quadratic equation instead of linear. In this problem, both sides have $3x^2$ , so they subtract to zero, leaving a simple linear equation.

Can I solve this without expanding first?

You must expand the left side to see what you're working with! Without expanding $(3x+4)(x+2)$ , you can't compare it properly to $3x^2 + 2$ on the right side.

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