Упр.22.14 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1) x^2-6xy+5y^2; 2) a^2+5ab-36b^2;
3) 3m^2-8mn-3n^2; 4) 4x^2-5xy+y^2.

1. $$x^2-6xy+5y^2=x^2-xy-5xy+5y^2=x(x-y)-5y(x-y)=(x-y)(x-5y).$$

2. $$a^2+5ab-36b^2=a^2+9ab-4ab-36b^2=a(a+9b)-4b(a+9b)=(a+9b)(a-4b).$$

3. $$3m^2-8mn-3n^2=3m^2-9mn+mn-3n^2=3m(m-3n)+n(m-3n)=(3m+n)(m-3n).$$

4. $$4x^2-5xy+y^2=4x^2-4xy-xy+y^2=4x(x-y)-y(x-y)=(4x-y)(x-y).$$

Ответ

1) $$ (x-y)(x-5y) $$; 2) $$ (a+9b)(a-4b) $$; 3) $$ (3m+n)(m-3n) $$; 4) $$ (4x-y)(x-y) $$.