Question

Разложите на множители:
а) х²-49
б) 4х²у²-9а⁴
в) 25а²-(а+3)²
г) 27m³+n³​
д) 25х²-10ху+у²

Answer 1

a) $x^2-49=x^2-7^2=(x-7)(x+7)$

б) $4x^2y^2-9a^4=2^2x^2y^2-3^2(a^2)^2=(2xy)^2-(3a^2)^2=(2xy-3a^2)(2xy+3a^2)$

в)

$25a^2-(a+3)^2=5^2a^2-(a+3)^2=(5a)^2-(a+3)^2=(5a - (a + 3))(5a + a + 3)=(5a-a-3)(5a+a+3)=(4a-3)(6a+3)$

г)$27m^3+n^3=3^3m^3+n^3=(3m)^3+n^3=(3m+n)((3m)^2-2*3mn+n^2)=(3m+n)(9m^2-6mn+n^2)$

д) $25x^2-10xy+y^2=5^2x^2-10xy+y^2=(5x^2)-2*5xy+y^2=(5x-y)^2$