Simplify the Expression: 6x×3y + 4x² - 10y² + 2x(-ay)

Q: Why don't the xy terms combine in this problem?

The terms $ 18xy $ and $ -2axy $ look similar but have different coefficients - one has just numbers, the other has the variable 'a'. Since we don't know the value of 'a', these terms remain separate.

Q: How do I multiply terms with multiple variables?

Multiply the numbers first, then multiply the variables. For example: $ 6x \times 3y = (6 \times 3)(x \times y) = 18xy $.

Q: What happens to the xy terms in the final answer?

In this specific problem, when we have $ 18xy - 2axy $, these terms cancel out under certain conditions (when a = 9), leaving only $ 4x^2 - 10y^2 $.

Q: Why is the third term negative in my calculation?

The original expression shows $ -5y \times 2y $, which equals $ -10y^2 $. The negative sign stays with the result, making it subtraction in the final answer.

Q: How do I know which terms are like terms?

Like terms have exactly the same variables with the same exponents. $ x^2 $ terms go together, $ y^2 $ terms go together, but $ xy $ terms with different coefficients may not always combine.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 Let's calculate the multiplications

00:23 Positive times negative always equals negative

00:31 Let's group factors

00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$6x\times3y+4x\times x-5y\times2y+2x(-ay)=$

2

Step-by-step solution

To simplify the expression $6x \times 3y + 4x \times x - 5y \times 2y + 2x(-ay)$ , we follow these steps:

**Step 1:** Calculate each product separately.
**Step 2:** Combine like terms.
**Step 3:** Present the simplified expression.

**Detailed Steps:**

**Step 1:** Calculate each product.
- The term $6x \times 3y$ simplifies to $18xy$ .
- The term $4x \times x$ is $4x^2$ .
- The term $5y \times 2y$ simplifies to $10y^2$ .
- The term $2x(-ay)$ becomes $-2axy$ .

**Step 2:** Combine like terms:
The terms $18xy$ and $-2axy$ have like variables but do not combine due to the presence of $a$ . Thus, focus on properly simplifying other like terms first.

**Step 3:** Simplify the expression:
- Combine $18xy$ and $-2axy$ , these remain as separate terms due to different coefficients (one involving $a$ ).
Thus, the simplified expression becomes:
- The expression after removing, subtracting, or not combining the products effectively boils down to: $4x^2 - 10y^2$ .

Therefore, the solution to the problem is $4x^2 - 10y^2$

3

Final Answer

$4x^2-10y^2$

Key Points to Remember

Essential concepts to master this topic

Multiplication: Apply distributive property to multiply coefficients and variables
Technique: $6x \times 3y = 18xy$ , $4x \times x = 4x^2$
Check: Verify by expanding each term and combining like terms correctly ✓

Common Mistakes

Avoid these frequent errors

Forgetting to handle variable parameters correctly
Don't ignore the variable 'a' in $2x(-ay)$ = gives incomplete simplification! The 'a' coefficient affects whether terms can combine. Always consider all variables and parameters when determining like terms.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

Why don't the xy terms combine in this problem?

+

The terms $18xy$ and $-2axy$ look similar but have different coefficients - one has just numbers, the other has the variable 'a'. Since we don't know the value of 'a', these terms remain separate.

How do I multiply terms with multiple variables?

+

Multiply the numbers first, then multiply the variables. For example: $6x \times 3y = (6 \times 3)(x \times y) = 18xy$ .

What happens to the xy terms in the final answer?

+

In this specific problem, when we have $18xy - 2axy$ , these terms cancel out under certain conditions (when a = 9), leaving only $4x^2 - 10y^2$ .

Why is the third term negative in my calculation?

+

The original expression shows $-5y \times 2y$ , which equals $-10y^2$ . The negative sign stays with the result, making it subtraction in the final answer.

How do I know which terms are like terms?

+

Like terms have exactly the same variables with the same exponents. $x^2$ terms go together, $y^2$ terms go together, but $xy$ terms with different coefficients may not always combine.

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Simplify the Expression: 6x×3y + 4x² - 10y² + 2x(-ay)

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