\(2xy^2+x^2y^4+1\\ =\left(xy^2\right)^2+2xy^2.1+1^2\\ =\left(xy^2+1\right)^2\)

Ta có :

\(2xy^2+x^2y^4+1=\left(xy^2\right)^2+2.xy^2.1+1^2\)

\(=\left(xy^2+1\right)^2\)

a, \(4x^2+4xy+y^2=\left(4x\right)^2+2.2x.y+y^2\)

\(=\left(4x+y\right)^2\)

b, \(9m^2+n^2-6mn=\left(3m\right)^2-2.3m.n+n^2\)

\(=\left(3m-n\right)^2\)

c, \(16a^2+25b^2+40ab=\left(4a\right)^2+2.4a.5b+\left(5b\right)^2\)

\(=\left(4a+5b\right)^2\)

d, \(x^2-x+\dfrac{1}{4}=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\)

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

Chúc bạn học tốt!!!

1. 2xy² +x²y⁴+1 = (xy²+1)²

2. a)3x²+3x-10x-10=3x(x+1)-10(x+1)=(x+1)(3x-10)

b)2x²-5x-7=2x²+2x-7x-7=2x(x+1)-7(x+1)=(x+1)(2x-7)

Mong có thể giúp được bạn

x² - 3x + 2
= x² - x - 2x + 2
= x(x - 1) - 2(x - 1)
= (x - 1)(x - 2)

3x² - 7x - 10
= 3x² + 3x - 10x - 10
= 3x(x + 1) - 10(x + 1)
= (x + 1)(3x - 10)

2x² - 5x - 7
= 2x² + 2x - 7x - 7
= 2x(x + 1) - 7(x + 1)
= (x + 1)(2x - 7)

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

b)\(\left(x-y+6\right)\left(x+y-6\right)=\left[x-\left(y-6\right)\right]\left(x+y-6\right)=x^2-\left(y-6\right)^2\)

\(a,\left(x+y+4\right)\left(x+y-4\right)\)
\(=\left(x+y\right)^2-4^2\)
\(b,\left(x-y+6\right)\left(x+y-6\right)\)
\(=x^2-\left(y-6\right)^2\)

\(\left(x+y+4\right)\left(x+y-4\right)\)

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

\(\left(x-y+6\right)\left(x-y-6\right)\)

\(=\left(x-y\right)^2-6^2\)

a) \(x^2-10\cdot2\cdot x+10^2=\left(x-10\right)^2\)

b) \(x^2+2\cdot5\cdot x+5^2=\left(x+5\right)^2\)

c) \(x^2-2\cdot6\cdot xy+\left(6y\right)^2=\left(x-6y\right)^2\)