Đáp án + Giải thích các bước giải:

Bài $15$:

$\textbf{a$\bigg)$} x^4 + 2019x^2 + 2018x + 2019$

$= x^4 - x^3 + x^3 + 2019x^2 - x^2 + x^2 + 2019x - x + 2019$

$= x^4 - x^3 + 2019x^2 + x^3 - x^2 + 2019x + x^2 - x + 2019$

$= x^2 (x^2 - x + 2019) + x(x^2 - x + 2019) + x^2 - x + 2019$

$= (x^2 + x + 1)(x^2 - x + 2019)$

$\textbf{b$\bigg)$} x^2 - 4x + 4y - 2xy + y^2 - 5$

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

$= (x - y)^2 - 4(x - y) - 5$

$= (x - y)^2 - 5(x - y) + (x - y) - 5$

$= (x - y + 1)(x - y - 5)$

Bài $16$:

$\textbf{a$\bigg)$} a^3 - a^2 - 4a + 4$

$= a^3 - 2a^2 + a^2 - 4a + 4$

$= a^2(a - 2) + (a - 2)^2$

$= (a^2 + a - 2)(a - 2)$

$\textbf{b$\bigg)$} 2a^3 + 7a^2b + 7ab^2 + 2b^3$

$= 2(a^3 + b^3) + 7ab(a + b)$

$= 2(a + b)(a^2 - ab + b^2) + 7ab(a + b)$

$= (2a^2 - 2ab + 2b^2 + 7ab)(a + b)$

$= (2a^2 + 5ab + 2b^2)(a + b)$

$= (2a^2 + 4ab + ab + 2b^2)(a + b)$

$= [2a(a + 2b) + b(a + 2b)](a + b)$

$= (2a + b)(a + 2b)(a + b)$