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\(b,16x^2-8x+1=\left(4x-1\right)^2\\ c,4x^2+12xy+9y^2=\left(2x+3y\right)^2\\ e,=x^2+2x+1+y^2+2y+1+2\left(x+1\right)\left(y+1\right)\\ =\left(x+1\right)^2+2\left(x+1\right)\left(y+1\right)+\left(y+1\right)^2\\ =\left[\left(x+1\right)+\left(y+1\right)\right]^2=\left(x+y+2\right)^2\\ g,=x^2-2x\left(y+2\right)+\left(x+2\right)^2=\left[x-\left(y+2\right)\right]^2=\left(x-y-2\right)^2\\ h,=\left[x+\left(y+1\right)\right]^2=\left(x+y+1\right)^2\)
a) ( x + 1 ) 2 . b) ( x – 4 ) 2 .
c) x 2 4 + x + 1 ; d) ( 2 x – 2 y ) 2 .
4x²y⁴ - 4xy³ + y²
= (2xy²)² - 2.2xy².y + y²
= (2xy² - y)²
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Sửa đề:
(x - 2y)² - 4(x - 2y) + 4
= (x - 2y)² - 2.(x - 2y).2 + 2²
= (x - 2y - 2)²
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25x² - 5xy + 1/4 y²
= (5x)² - 2.5xy.y/2 + (y/2)²
= (5x - y/2)²
\(4x^2y^4-4xy^3+y^2\)
\(=\left(2xy^2\right)^2-2\cdot2xy^2\cdot y+y^2\)
\(=\left(2xy^2-y\right)^2\)
_____
\(\left(x-2y\right)^2-4\left(x-2y\right)+4\)
\(=\left(x-2y\right)^2-2\cdot\left(x-2y\right)\cdot2+2^2\)
\(=\left[\left(x-2y\right)-2\right]^2\)
\(=\left(x-2y-2\right)^2\)
____
\(25x^2-5xy+\dfrac{1}{4}y^2\)
\(=\left(5x\right)^2-2\cdot\dfrac{5}{2}xy+\left(\dfrac{1}{2}y\right)^2\)
\(=\left(5x\right)^2-2\cdot\dfrac{1}{2}y\cdot5x+\left(\dfrac{1}{2}y\right)^2\)
\(=\left(5x-\dfrac{1}{2}y\right)^2\)
a)\(x^2+2x+1=x^2+2x1+1^2=\left(x+1\right)^2\)
b)\(9x^2+y^2+6xy=3^2x^2+y^2+2.3x.y=\left(3x\right)^2+2.3x.y+y^2=\left(3x+y\right)^2\)
c)\(25a^2+4b^2-20ab=5^2a^2+2^2b^2-2.5a.2b=\left(5a\right)^2-2.5a.2b+\left(2b\right)^2=\left(5a-2b\right)^2\)
d)\(x^2-x+\frac{1}{4}=x^2-2.x.\frac{1}{2}+\left(\frac{1}{2}\right)^2=\left(x-\frac{1}{2}\right)^2\)
a) \(x^2+2x+1=\left(x+1\right)^2\)
b) \(9x^2+y^2+6xy=\left(3x+y\right)^2\)
c) \(25a^2+4b^2-20ab=\left(5a-2b\right)^2\)
Câu d thì biểu thức là \(\frac{x^2-1}{2x+\frac{1}{10}}\) hay là \(\frac{x^2-1}{\frac{2x+1}{10}}\) z bạn???
a. $x^2+4x+4$
$=x^2+2\cdot x\cdot2+2^2$
$=(x+2)^2$
b. $x^2-6xy+9y^2$
$=x^2-2\cdot x\cdot3y+(3y)^2$
$=(x-3y)^2$
c. $4x^2+12x+9$
$=(2x)^2+2\cdot2x\cdot3+3^2$
$=(2x+3)^2$
d. $x^2-x+\dfrac14$
$=x^2-2\cdot x\cdot \dfrac12+\Bigg(\dfrac12\Bigg)^2$
$=\Bigg(x-\dfrac12\Bigg)^2$
a) Sửa đề: \(x^2+3x+1\rightarrow x^2+2x+1\)
\(x^2+2x+1=\left(x+1\right)^2\)
b) \(x^2+y^2+2xy=\left(x+y\right)^2\)
c) \(9x^2+12x+4=\left(3x+2\right)^2\)
d) \(-4x^2-9-12x=-\left(4x^2+12x+9\right)=-\left(2x+3\right)^2\)
a/ (y+1)2
b/ (3x-y)2
c/ (5a+2b)2
d/ (x-1/2)2