Question

1.(xy+x²y²)(x²y+xy²) 2.(2a²-5b²)(3a²+4b²) 3.(5x²-6y²)(6x²-5y²) 4.(x²+2x+1)(x+3)

Answer 1

1. (xy + x²y²)(x²y + xy²) = x³y² + x²y³ + x⁴y³ + x³y⁴
2. (2a² - 5b²)(3a² + 4b²) = 6a⁴ + 8a²b² - 15a²b² - 20b⁴ = 6a⁴ - 7a²b² - 20b⁴
3. (5x² - 6y²)(6x² - 5y²) = 30x⁴ - 25x²y² - 36y⁴ + 30x²y² = 30x⁴ + 5x²y² - 36y⁴
4. (x² + 2x + 1)(x + 3) = x³ + 2x² + x + 3x² + 6x + 3 = x³ + 5x² + 7x + 3

Answer 2

Sure, I can help you with that. Let's go through each expression step by step.

1. (xy + x²y²)(x²y + xy²)

To simplify this expression, we can use the distributive property of multiplication. We will multiply each term in the first set of parentheses with each term in the second set of parentheses, and then combine like terms.

Let's start by multiplying the first term in the first set of parentheses (xy) with each term in the second set of parentheses: (xy)(x²y) = x³y² (xy)(xy²) = x²y³

Next, let's multiply the second term in the first set of parentheses (x²y²) with each term in the second set of parentheses: (x²y²)(x²y) = x⁴y⁴ (x²y²)(xy²) = x³y⁴

Now, let's combine all the terms we obtained: x³y² + x²y³ + x⁴y⁴ + x³y⁴

This is the simplified form of the expression (xy + x²y²)(x²y + xy²).

2. (2a² - 5b²)(3a² + 4b²)

Similarly, we can use the distributive property to simplify this expression.

Let's start by multiplying the first term in the first set of parentheses (2a²) with each term in the second set of parentheses: (2a²)(3a²) = 6a⁴ (2a²)(4b²) = 8a²b²

Next, let's multiply the second term in the first set of parentheses (-5b²) with each term in the second set of parentheses: (-5b²)(3a²) = -15a²b² (-5b²)(4b²) = -20b⁴

Now, let's combine all the terms we obtained: 6a⁴ + 8a²b² - 15a²b² - 20b⁴

Simplifying further, we have: 6a⁴ - 7a²b² - 20b⁴

This is the simplified form of the expression (2a² - 5b²)(3a² + 4b²).

3. (5x² - 6y²)(6x² - 5y²)

Again, we will use the distributive property to simplify this expression.

Let's start by multiplying the first term in the first set of parentheses (5x²) with each term in the second set of parentheses: (5x²)(6x²) = 30x⁴ (5x²)(-5y²) = -25x²y²

Next, let's multiply the second term in the first set of parentheses (-6y²) with each term in the second set of parentheses: (-6y²)(6x²) = -36x²y² (-6y²)(-5y²) = 30y⁴

Now, let's combine all the terms we obtained: 30x⁴ - 25x²y² - 36x²y² + 30y⁴

Simplifying further, we have: 30x⁴ - 61x²y² + 30y⁴

This is the simplified form of the expression (5x² - 6y²)(6x² - 5y²).

4. (x² + 2x + 1)(x + 3)

To simplify this expression, we will use the distributive property once again.

Let's start by multiplying the first term in the first set of parentheses (x²) with each term in the second set of parentheses: (x²)(x) = x³ (x²)(3) = 3x²

Next, let's multiply the second term in the first set of parentheses (2x) with each term in the second set of parentheses: (2x)(x) = 2x² (2x)(3) = 6x

Finally, let's multiply the third term in the first set of parentheses (1) with each term in the second set of parentheses: (1)(x) = x (1)(3) = 3

Now, let's combine all the terms we obtained: x³ + 3x² + 2x² + 6x + x + 3

Simplifying further, we have: x³ + 5x² + 7x + 3

This is the simplified form of the expression (x² + 2x + 1)(x + 3).

I hope this helps! Let me know if you have any further questions.