\(1,=x^2+4xy+4y^2\)
\(2,=4x^2+12xy+9y^2\\ 3,=9x^2-12xy+4y^2\\ 4,=25x^2-10xy+y^2\\ 5,=x^2+2.x.\dfrac{1}{4}+\dfrac{1}{16}=x^2+\dfrac{1}{2}x+\dfrac{1}{16}\\ 6,=4x^2-2.2x.\dfrac{1}{2}+\dfrac{1}{4}=4x^2-2x+\dfrac{1}{4}\\ 7,=\dfrac{1}{9}x^2-2.\dfrac{1}{3}x.\dfrac{1}{2}y+\dfrac{1}{4}y^2\\ =\dfrac{1}{9}x^2-\dfrac{1}{3}xy+\dfrac{1}{4}y^2\)
1: \(=x^2+4xy+4y^2\)
2: \(=4x^2+12xy+9y^2\)
3: \(=9x^2-12xy+4y^2\)
4: \(=25x^2-10xy+y^2\)
5: \(=x^2+\dfrac{1}{2}x+\dfrac{1}{16}\)
`1)(x+2y)^2=x^2 + 4xy +4y^2`
`2)(2x+3y)^2= 4x^2 + 12xy+9y^2`
`3)(3x-2y)^2=9x^2 - 12xy +4y^2`
`4)(5x-y)^2 =25x^2 -10xy + y^2`
`5)(x+ 1/4)^2 = x^2 + 1/2 x + 1/16`
`6)(2x-1/2)^2 = 4x^2 - 2x + 1/4`
`7)(1/3x - 1/2y)^2 = 1/9 x^2 -1/3 xy + 1/4 y^2`
1) (x + 2y)² = x² + 2.x.2y + (2y)² = x² + 4xy + 4y²
2) (2x + 3y)² = (2x)² + 2.2x.3y + (3y)² = 4x² + 12xy + 9y²
3) (3x - 2y)² = (3x)² - 2.3x.2y + (2y)² = 9x² - 12xy + 4y²
4) (5x - y)² = (5x)² - 2.5x.y + y² = 25x² - 10xy + y²
5) (x + 1/4)² = x² + 2.x.1/4 + (1/4)²
= x² + x/2 + 1/16
6) (2x - 1/2)² = (2x)² - 2.2x.1/2 + (1/2)² = 4x² - 2x + 1/4
7) (1/3 x - 1/2 y)² = (1/3 x)² - 2.1/3 x.1/2 y + (1/2 y)² = 1/9 x² - 1/3 xy + 1/4 y²