Question

calcule ( produtos notáveis )

a)(2x+1/2)²=
b)( x/2 +y/2)²=
c) (3y+3x)²=

por favor me ajudem

Answer 1

A)

$(2x + \frac{1}{2} ) ^{2} = (2x + \frac{1}{2} )(2x + \frac{1}{2} ) \\ 4 {x}^{2} + (2x \times \frac{1}{2}) + ( \frac{1}{2} \times 2x) + \frac{1}{4}$

Temos que

$2x \times \frac{1}{2} = \frac{2x}{2} = x$

Então

$4 {x}^{2} + x + x + \frac{1}{4} \\ 4 {x}^{2} + 2x + \frac{1}{4}$

B)

$( \frac{x}{2} + \frac{y}{2} )^{2} =( \frac{x}{2} + \frac{y}{2} )( \frac{x}{2} + \frac{y}{2} ) \\ \frac{x}{2} \times \frac{x}{2} + \frac{x}{2} \times \frac{y}{2} + \frac{y}{2} \times \frac{x}{2} + \frac{y}{2} \times \frac{y}{2}$

Temos que

$\frac{x}{2} \times \frac{x}{2} = \frac{ {x}^{2} }{4}$

$\frac{x}{2} \times \frac{y}{2} = \frac{xy}{4}$

$\frac{y}{2} \times \frac{y}{2} = \frac{ {y}^{2} }{4}$

Então

$\frac{ {x}^{2} }{4} + \frac{xy}{4} + \frac{xy}{4} + \frac{ {y}^{2} }{4 } = \\ \frac{ {x}^{2} }{4} + \frac{xy}{2} + \frac{ {y}^{2} }{4}$

C)

${(3y + 3x)}^{2} = (3y + 3x)(3y + 3x) \\ {3y}^{2} + 9xy + 9xy + {3x}^{2} \\ {3x}^{2} + {3y}^{2} + 18xy$