Question

Subtract the sum of 4x² + 7xy + 3y² + 1 and 2x² - 5xy - 2y² + 8 from 9x² - 8xy + 11y²?

Answer 1

To subtract the given polynomials, we first need to combine like terms.

The given polynomials are:
\( 4x^{4} + 7xy + 3y^{2} + 1 \) and
\( 2x^{2} - 5xy - 2y^{2} + 8 \).

Step 1: Combine the like terms for \( x^{4} \).
There is only one term with \( x^{4} \), so we bring it down as is: \( 4x^{4} \).

Step 2: Combine the like terms for \( x^{2} \).
The given polynomials have \( x^{2} \) terms, but they have different coefficients. So we subtract them:
\( 2x^{2} - 5x^{2} = -3x^{2} \).

Step 3: Combine the like terms for \( xy \).
The given polynomials have \( xy \) terms, but they have different coefficients. So we subtract them:
\( 7xy - (-5xy) = 7xy + 5xy = 12xy \).

Step 4: Combine the like terms for \( y^{2} \).
The given polynomials have \( y^{2} \) terms, but they have different coefficients. So we subtract them:
\( 3y^{2} - (-2y^{2}) = 3y^{2} + 2y^{2} = 5y^{2} \).

Step 5: Combine the constant terms.
The given polynomials have constant terms, but they have different coefficients. So we subtract them:
\( 1 - 8 = -7 \).

Therefore, the subtracted form of \( 4x^{4} + 7xy + 3y^{2} + 1 \) and \( 2x^{2} - 5xy - 2y^{2} + 8 \) from \( 9x^{2} + 8xy + 11y^{2} \) is:
\( 4x^{4} - 3x^{2} + 12xy + 5y^{2} - 7 \).

Hope this helped<3

Answer 2

To subtract the given polynomials, first sum up 4x² + 7xy + 3y² + 1 and 2x² - 5xy - 2y² + 8 to get 6x² + 2xy + y² + 9. Then, subtract this from 9x² - 8xy + 11y² to get the final result: 3x² - 10xy + 10y² - 9.

Step-by-step explanation:

To subtract the sum of 4x² + 7xy + 3y² + 1 and 2x² - 5xy - 2y² + 8 from 9x² - 8xy + 11y², we first need to calculate the sum of the two polynomials and then subtract the result from the third polynomial.

First, we find the sum:

• 4x² + 2x² = 6x²
• 7xy - 5xy = 2xy
• 3y² - 2y² = 1y²
• 1 + 8 = 9

The sum is 6x² + 2xy + y² + 9.

Next, we subtract this sum from the polynomial 9x² - 8xy + 11y²:

• 9x² - 6x² = 3x²
• -8xy - 2xy = -10xy
• 11y² - y² = 10y²
• 0 - 9 = -9

The result of the subtraction is 3x² - 10xy + 10y² - 9.