Câu $1$.
$a$) $(x+2y)^2 = x^2 + 2.x.2y + (2y)^2 = x^2 + 4xy + 4y^2$
$b$) $(3x-2y)^2 = (3x)^2 - 2.2x.2y + (2y)^2 = 9x^2 - 8xy + 4y^2$
$c$) `(2x- 1/2)^3 = (2x)^3 - 3.(2x)^2. 1/2 + 3.2x. (1/2)^2 - (1/2)^3= 8x^3 - 6x^2 + 3/2 x - 1/8`
$d$) `(x/2 - y)(x/2 + y) = (x/2)^2 - y^2 = {x^2}/4 - y^2`
$e$) `(x+1/3)^3 = x^3 + 3.x^2. 1/3 + 3.x . (1/3)^2 + (1/3)^3 = x^3 + x^2 + x/3 + 1/{27}`
$f$) $(x-2)(x^2+2x+4) = x^3 - 2^3 = x^3 - 8$.
Câu $2$.
$a$) $x^3 + 8y^3 = x^3 + (2y)^3 = (x+2y)(x^2-2xy + 4y^2)$.
$b$) $a^6 - b^3 = (a^2)^3 - b^3 = (a^2 - b)(a^4 + a^2b + b^2)$.
$c$) $8y^3 - 125 = (2y)^3 - 5^3 = (2y-5)(4y^2 + 10y + 25)$.
Câu $3$.
$a$) $(x-10)^2 - x(x+80)$
$= x^2 - 20x + 100 - x^2 - 80x$
$= -100x + 100$
$= 100-100x$
$= 100(1-x)$
Thay $x=0,98$ vào ta được $100.(1-0,98) =100.0,02 = 2$.
$b$) $(2x+9)^2 - x(4x+31) $
$= 4x^2 + 36x + 81 - 4x^2 - 31x$
$= 5x + 81$
Thay $x=-16,2$ vào ta được $5.(-16,2)+81=-81+81=0$.
$c$) $4x^2 - 28x + 49$
$= (2x)^2 - 2.2x.7 + 7^2$
$= (2x-7)^2$
Thay $x=4$ vao ta được : $(2.4-7)^2 = 1^2=1$.
$d$) $x^3 - 9x^2 + 27x - 27$
$= x^3 - 3.x^2.3 + 3.x.3^2 - 3^3$
$= (x-3)^3$
Thay $x=5$ vào ta được : $(5-3)^3 = 2^3 = 8$.
Câu $4$.
$a$) $(x-3)^2 - 4 = 0$
$⇔ (x-3)^2 = 4 = (±2)^2$
$⇒$ \(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\)
Vậy $x$ $∈$ `{1;5}`.
