Questions: (x^3+7xy+6y^2)-(2x^3+2xy+7y^2) (x^3+7xy+6y^2)-(2x^3+2xy+7y^2)=

(x^3+7xy+6y^2)-(2x^3+2xy+7y^2)
(x^3+7xy+6y^2)-(2x^3+2xy+7y^2)=

Transcript text: \[ \begin{array}{c} \left(x^{3}+7 x y+6 y^{2}\right)-\left(2 x^{3}+2 x y+7 y^{2}\right) \\ \left(x^{3}+7 x y+6 y^{2}\right)-\left(2 x^{3}+2 x y+7 y^{2}\right)= \end{array} \]

Solution

Solution Steps

To solve the given algebraic expression, we need to subtract the second polynomial from the first polynomial. This involves subtracting the coefficients of like terms.

Solution Approach

Identify and align the like terms in both polynomials.
Subtract the coefficients of the like terms.
Combine the results to form the final polynomial.

Step 1: Define the Polynomials

We start with the two polynomials: \[ P_1 = x^3 + 7xy + 6y^2 \] \[ P_2 = 2x^3 + 2xy + 7y^2 \]

Step 2: Subtract the Polynomials

Next, we perform the subtraction \( P_1 - P_2 \): \[ P_1 - P_2 = (x^3 + 7xy + 6y^2) - (2x^3 + 2xy + 7y^2) \]

Step 3: Combine Like Terms

Now, we combine the like terms: \[ = x^3 - 2x^3 + 7xy - 2xy + 6y^2 - 7y^2 \] \[ = -x^3 + 5xy - y^2 \]

Final Answer

The result of the subtraction is: \[ \boxed{-x^3 + 5xy - y^2} \]

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