Question

преобразуйте в многочлен выражение (а+b)^2(a-b)

Answer 1

(a+b)^2= a^2+b^2+2ab

(a^2+b^2+2ab)(a-b)=a в 3 степни- a^2+ab^2-b в степени 3+2a^2b-2ab^2

Answer 2

Converting the Expression to a Polynomial

To convert the expression (a+b)^2(a-b) into a polynomial, we can expand it using the distributive property and simplify the terms.

The given expression can be expanded as follows:

(a+b)^2(a-b) = (a+b)(a+b)(a-b)

Expanding the first two terms using the distributive property:

(a+b)(a+b) = a(a+b) + b(a+b)

Simplifying the terms:

= a^2 + ab + ab + b^2

Combining like terms:

= a^2 + 2ab + b^2

Now, we can substitute this result back into the original expression:

(a+b)^2(a-b) = (a^2 + 2ab + b^2)(a-b)

Expanding this expression using the distributive property:

= a^2(a-b) + 2ab(a-b) + b^2(a-b)

Simplifying the terms:

= a^3 - a^2b + 2a^2b - 2ab^2 + ab^2 - b^3

Combining like terms:

= a^3 + a^2b - 2ab^2 + ab^2 - b^3

Therefore, the polynomial expression for (a+b)^2(a-b) is a^3 + a^2b - 2ab^2 + ab^2 - b^3.

Please let me know if there's anything else I can help you with!