Question

3) 7x³y²( -4x²y³ +1,5xy²-4y⁴)​

Answer 1

7x³y²( -4x²y³ +1,5xy²-4y⁴)

-7x³y²×4x²y³ +7x 3.2 ²×1,5xy²-7x³y²2x4y⁴

-28х⁵у⁵+10,5х⁴у⁴-28х³у⁶

Answer 2

To simplify the expression 7x³y²(-4x²y³ + 15xy² - 4y⁴), you can use the distributive property to multiply each term inside the parentheses by 7x³y²:

7x³y² * (-4x²y³) + 7x³y² * 15xy² - 7x³y² * 4y⁴

Now, let's simplify each term:

1. 7x³y² * (-4x²y³): When you multiply the coefficients (7 and -4), you get -28. When you multiply the x terms (x³ and x²), you add their exponents, which gives you x^(3+2) = x^5. Similarly, when you multiply the y terms (y² and y³), you add their exponents, which gives you y^(2+3) = y^5. So, this term simplifies to -28x^5y^5.

2. 7x³y² * 15xy²: When you multiply the coefficients (7 and 15), you get 105. When you multiply the x terms (x³ and x), you add their exponents, which gives you x^(3+1) = x^4. Similarly, when you multiply the y terms (y² and y²), you add their exponents, which gives you y^(2+2) = y^4. So, this term simplifies to 105x^4y^4.

3. 7x³y² * 4y⁴: When you multiply the coefficients (7 and 4), you get 28. You multiply the x terms (x³ and there are no x terms in 4y⁴, so you get x³). When you multiply the y terms (y² and y⁴), you add their exponents, which gives you y^(2+4) = y^6. So, this term simplifies to 28x³y^6.

Now, you can combine these simplified terms:

-28x^5y^5 + 105x^4y^4 - 28x³y^6

This is the simplified expression for 7x³y²(-4x²y³ + 15xy² - 4y⁴).