Question

A)(x^2+7xy+3y^2)-(x^2+3y^2)^2= b)(a-b)(a^2-c^2)-(a-c)(a^2-b^2)= c)(x+y)^2-10(x^2-y^2)+25(x-y)^2= Тождества: a^3+b^3+3ab(a+b)=(a+b)^3

Answer 1

Ответ на фотографии

Answer 2

a) Let's simplify the expression (x^2 + 7xy + 3y^2) - (x^2 + 3y^2)^2:

(x^2 + 7xy + 3y^2) - (x^2 + 3y^2)^2 = x^2 + 7xy + 3y^2 - (x^2 + 6xy + 9y^2) = x^2 + 7xy + 3y^2 - x^2 - 6xy - 9y^2 = x^2 - x^2 + 7xy - 6xy + 3y^2 - 9y^2 = xy - 6xy - 6y^2 = -5xy - 6y^2

So the simplified expression is -5xy - 6y^2.

b) Let's simplify the expression (a - b)(a^2 - c^2) - (a - c)(a^2 - b^2):

(a - b)(a^2 - c^2) - (a - c)(a^2 - b^2) = a(a^2 - c^2) - b(a^2 - c^2) - a(a^2 - b^2) + c(a^2 - b^2) = a^3 - ac^2 - a^3 + ab^2 - a^3 + bc^2 + ca^2 - cb^2 = ab^2 - cb^2 + ca^2 - ac^2 = b^2(a - c) + c^2(a - c) = (b^2 + c^2)(a - c)

So the simplified expression is (b^2 + c^2)(a - c).

c) Let's simplify the expression (x + y)^2 - 10(x^2 - y^2) + 25(x - y)^2:

(x + y)^2 - 10(x^2 - y^2) + 25(x - y)^2 = (x^2 + 2xy + y^2) - 10(x^2 - y^2) + 25(x^2 - 2xy + y^2) = x^2 + 2xy + y^2 - 10x^2 + 10y^2 + 25x^2 - 50xy + 25y^2 = -9x^2 + 2xy + 36y^2 - 50xy + 25x^2 + 26y^2 = 16y^2 - 48x^2 - 48xy + 2xy = 16y^2 - 48x^2 - 46xy

So the simplified expression is 16y^2 - 48x^2 - 46xy.