a) Ta có: \(25x^2-20x+7\)

\(=\left(5x\right)^2-2\cdot5x\cdot2+4+3\)

\(=\left(5x-2\right)^2+3\ge3\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{2}{5}\)

b) Ta có: \(9x^2-6x+2\)

\(=9x^2-6x+1+1\)

\(=\left(3x-1\right)^2+1\ge1\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{1}{3}\)

c) Ta có: \(-x^2+2x-2\)

\(=-\left(x^2-2x+2\right)\)

\(=-\left(x^2-2x+1+1\right)\)

\(=-\left(x-1\right)^2-1\le-1\forall x\)

Dấu '=' xảy ra khi x-1=0

hay x=1

d) Ta có: \(x^2+12x+39\)

\(=x^2+12x+36+3\)

\(=\left(x+6\right)^2+3\ge3\forall x\)

Dấu '=' xảy ra khi x=-6

e) Ta có: \(-x^2-12x\)

\(=-\left(x^2+12x+36-36\right)\)

\(=-\left(x+6\right)^2+36\le36\forall x\)

Dấu '=' xảy ra khi x=-6

f) Ta có: \(4x-x^2+1\)

\(=-\left(x^2-4x-1\right)\)

\(=-\left(x^2-4x+4-5\right)\)

\(=-\left(x-2\right)^2+5\le5\forall x\)

Dấu '=' xảy ra khi x=2

a) Ta có: \(25x^2-20x+7\)

\(=\left(5x\right)^2-2\cdot5x\cdot2+4+3\)

\(=\left(5x-2\right)^2+3\ge3\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{2}{5}\)

b) Ta có: \(9x^2-6x+2\)

\(=9x^2-6x+1+1\)

\(=\left(3x-1\right)^2+1\ge1\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{1}{3}\)

c) Ta có: \(-x^2+2x-2\)

\(=-\left(x^2-2x+2\right)\)

\(=-\left(x^2-2x+1+1\right)\)

\(=-\left(x-1\right)^2-1\le-1\forall x\)

Dấu '=' xảy ra khi x=1

( Mình trình bày mẫu câu a các câu khác mình làm tắt lại nhưng tương tự trình bày câu a nha )

a, Ta có : \(25x^2-20x+7=\left(5x\right)^2-2.5x.2+2^2+3\)

\(=\left(5x-2\right)^2+3\)

Thấy : \(\left(5x-2\right)^2\ge0\forall x\in R\)

\(\Rightarrow\left(5x-2\right)^2+3\ge3\forall x\in R\)

Vậy \(Min=3\Leftrightarrow5x-2=0\Leftrightarrow x=\dfrac{2}{5}\)

b, \(=9x^2-2.3x+1+1=\left(3x-1\right)^2+1\ge1\)

Vậy Min = 1 <=> x = 1/3

c, \(=-x^2+2x-1-1=-\left(x^2-2x+1\right)-1=-\left(x-1\right)^2-1\le-1\)

Vậy Max = -1 <=> x = 1

d, \(=x^2+2.x.6+36+3=\left(x+6\right)^2+3\ge3\)

Vậy Min = 3 <=> x = - 6

e, \(=-x^2-2.x.6-36+36=-\left(x+6\right)^2+36\le36\)

Vậy Max = 36 <=> x = -6 .

f, \(=-x^2+4x-4+5=-\left(x^2-4x+4\right)+5=-\left(x-2\right)^2+5\le5\)

Vậy Max = 5 <=> x = 2

Chọn B

Hoàn thiện HĐT ta thu được các đơn thức cần điền vào “…”.

a)  x 2 + 4x + 4 = ( x   +   2 ) 2 .           b) 4 x 2 – 12x + 9 = ( 2 x   –   3 ) 2 .

c) 4 x 2  – 12xy + 9 y 2 = ( 2 x   –   3 y ) 2 .

Chú ý: phép trừ ta chuyển thành cộng đại số.

d)  x − y 2 x + y 2 = x 2 − y 2 4 .

a,2²;x;2

b,12x;3x;2

c,(1/2)²;x;1/2

d,?

a) \(x^2+4x+4=\left(x+2\right)^2\)

b) \(9x^2-12x+4=\left(3x-2\right)^2\)

c) \(x^2+x+\dfrac{1}{4}=\left(x+\dfrac{1}{2}\right)^2\)

a: \(\left(x+2\right)^2=x^2+2\cdot x\cdot2+2^2=x^2+4x+4\)

b: \(\left(2x+y\right)^2=\left(2x\right)^2+2\cdot2x\cdot y+y^2=4x^2+4xy+y^2\)

c: \(\left(x-3y\right)^2=x^2-2\cdot x\cdot3y+\left(3y\right)^2=x^2-6xy+9y^2\)

d: \(\left(\dfrac{1}{2}x-y\right)^2=\left(\dfrac{1}{2}x\right)^2-2\cdot\dfrac{1}{2}x\cdot y+y^2\)

\(=\dfrac{1}{4}x^2-xy+y^2\)

e: \(\left(x^2-y\right)^2=\left(x^2\right)^2-2\cdot x^2y+y^2=x^4-2x^2y+y^2\)

a) \(\left(x+2\right)^2\)

\(=x^2+2\cdot x\cdot2+2^2\)

\(=x^2+4x+4\)

b) \(\left(2x+y\right)^2\)

\(=\left(2x\right)^2+2\cdot2x\cdot y+y^2\)

\(=4x^2+4xy+y^2\)

c) \(\left(x-3y\right)^2\)

\(=x^2-2\cdot x\cdot3y+\left(3y\right)^2\)

\(=x^2-6xy+9y^2\)

d) \(\left(\dfrac{1}{2}x-y\right)^2\)

\(=\left(\dfrac{1}{2}x\right)^2-2\cdot\dfrac{1}{2}x\cdot y+y^2\)

\(=\dfrac{x^2}{4}-xy+y^2\)

e) \(\left(x^2-y\right)^2\)

\(=\left(x^2\right)^2-2\cdot x^2\cdot y+y^2\)

\(=x^4-2x^2y+y^2\)

a)(x+2)²=x²+2×x×2+2²=x²+4x+2

b)(2x+y)²=(2x)²+2×2x×y+y²=4x²+4xy+y²

c)(x-3y)²=x²-2×x×3y+(3y)²=x²-6xy+9y

d)(1/2x-y)²=(1/2x)²-2×1/2x×y+y²=1/4x²-xy+y²

e)(x²-y)²=(x²)²-2×x²×y+y²=x⁴-2x²y+y²

a) \(\left(2x+3y\right)^2=\left(2x\right)^2+2\cdot2x\cdot3y+\left(3y\right)^2=4x^2+12xy+9y^2\)

b) \(\left(x+\dfrac{1}{4}\right)^2=x^2+2\cdot x\cdot\dfrac{1}{4}+\left(\dfrac{1}{4}\right)^2=x^2+\dfrac{1}{2}x+\dfrac{1}{16}\)

c) \(\left(x^2+\dfrac{2}{5}y\right)\left(x^2-\dfrac{2}{5}y\right)=\left(x^2\right)^2-\left(\dfrac{2}{5}y\right)^2=x^4-\dfrac{4}{25}y^2\)

d) \(\left(2x+y^2\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y^2+3\cdot2x\cdot\left(y^2\right)^2+\left(y^2\right)^3=8x^3+12x^2y^2+6xy^4+y^6\)

e) \(\left(3x^2-2y\right)^2=\left(3x^2\right)^2-2\cdot3x^2\cdot2y+\left(2y\right)^2=9x^4-12x^2y+4y^2\)

f) \(\left(x+4\right)\left(x^2-4x+16\right)=x^3+4^3=x^3+64\)

g) \(\left(x^2-\dfrac{1}{3}\right)\cdot\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)=\left(x^2\right)^3-\left(\dfrac{1}{3}\right)^3=x^6-\dfrac{1}{27}\)

Mình cần gấp ạk

A và B

nhìu giữ cha !!!!

a.

$12x^3y-24x^2y^2+12xy^3=12xy(x^2-2xy+y^2)=12xy(x-y)^2$
b.

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

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

d.

$x^3-3x^2+3x-1=(x-1)^3$

e.

$3x^2-3y^2-12x-12y=(3x^2-3y^2)-(12x+12y)$

$=3(x-y)(x+y)-12(x+y)=(x+y)[3(x-y)-12]=3(x-y)(x-y-4)$

f.

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

g.

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

h. Không phân tích được thành nhân tử

i.

$x^2-2x-3=(x^2-3x)+(x-3)=x(x-3)+(x-3)=(x+1)(x-3)$

j.

$x^2+4x-12=(x^2-2x)+(6x-12)=x(x-2)+6(x-2)=(x-2)(x+6)$

k.

$x^2-8x-9=(x^2+x)-(9x+9)=x(x+1)-9(x+1)=(x+1)(x-9)$

l.

$x^2+x-6=(x^2+3x)-(2x+6)=x(x+3)-2(x+3)=(x-2)(x+3)$