Question

№ 3. Розкладіть на множники:

1) a + b + a ^ 2 - b ^ 2;
2 ) x ^ 2 - 2xy + y ^ 2 - m ^ 2 ;
3) (2m - 3) ^ 2 - (m + 2) ^ 2
СРОЧНО ДАЮ 50 БАЛОВ

Answer 1

a + b + a^2 - b^2 can be rewritten as (a^2 + a) - (b^2 - b), and then factored as (a+1)(a-b+1).
x^2 - 2xy + y^2 - m^2 can be factored as (x-y)^2 - m^2.
(2m-3)^2 - (m+2)^2 can be simplified as (2m-3+m+2)(2m-3-m-2), which becomes (3m-1)(-m-5), and then factored as (3m-1)(5+m).
Therefore, the factored forms of the given expressions are:

(a+1)(a-b+1)
(x-y)^2-m^2
(3m-1)(m+5) or (5+m)(3m-1).