Question

Разложите на множители, заменяя средний член на сумму одночленов

Answer 1

A² - 4ab + 3b² = a² - (ab + 3ab) + 3b² = (a² - ab) - (3ab - 3b²) = 
= a(a - b) - 3b(a - b) = (a - b)(a - 3b)

x² + 7xy - 8y² = x² + (8xy-xy) - 8y² =  (x² - xy) + (8xy - 8y²) =
= x(x-y) + 8y(x-y) = (x-y)(x+8y)

2x² - 5xy + 3y² = 2x² - (2xy + 3xy) + 3 y² = 2x² - 2xy - 3xy + 3 y² =
= (2x² - 2xy) - (3xy - 3y²) = 2x(x - y) - 3y(x - y) =
= (x - y)(2x - 3y)

Answer 2

Г) $a^{2} -4ab+3 b^{2} =a^{2} -3ab-ab+3 b^{2} =a(a-3b)-b(a-3b)= \\ =(a-b)(a-3b)$

д) $x^{2} +7xy-8y^{2} =x^{2} +8xy-xy-8y^{2} =x(x+8y)-y(x+8y)= \\ =(x-y)(x+8y)$

е) $2 x^{2} -5xy+3y^{2} =2 x^{2} -2xy-3xy+3y^{2} =2x(x-y)-3y(x-y)= \\ =(2x-3y)(x-y)$