Question

Разложите на множители 1) x-3y+x^2-9y^2= 2) 9m^2+6mn+n^2-25= 3) ab^5-b^5-ab^3+b^3= 4) 1-x^2+10xy-25y^=

Answer 1

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Answer 2

1. x-3y+x^2-9y^2 = (x^2-9y^2) + (x-3y) = (x+3y)(x-3y)+(x-3y)=(x-3y)(x+3y+1)

2. 9m^2+6mn+n^2-25 = (3m+n)^2 - 5^2 = (3m+n+5)(3m+n-5)

3. ab^5-b^5-ab^3+b^3 = b^3(a^1-a^0) - b^5(a^0-a^-1) = b^3(a-1)(a^2+a+1) - b^3(a^2+a+1)(a+1) = b^3(a-1)(a^2+a+1)(1-a)

4. 1-x^2+10xy-25y^2 = (1-5y-x)(1+5y+x)