Question

dau coroana,..........​

Answer 1

Explicație pas cu pas:

$\boxed {(a \pm b)^{2} = a^{2} \pm 2ab + b^{2}}$

a)

$(x + 2y)^{2} = x^{2} + 2 \cdot x \cdot (2y) + (2y)^{2} = x^{2} + 4xy + 4y^{2}$

b)

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

c)

$(3a + 2b)^{2} = (3a)^{2} + 2 \cdot (3a) \cdot (2b) + (2b)^{2} = 9a^{2} + 12ab + 4b^{2}$

d)

${( {x}^{2} + {y}^{2} )}^{2} = ( {x}^{2} )^{2} + 2 \cdot {x}^{2} \cdot {y}^{2} + ( {y}^{2} )^{2} = x^{4} + 2{x}^{2}{y}^{2} + y^{4}$

e)

${( 2{x}^{2} - 5{y}^{2} )}^{2} = (2 {x}^{2} )^{2} - 2 \cdot (2{x}^{2}) \cdot (5{y}^{2}) + ( 5{y}^{2} )^{2} = 4x^{4} - 20{x}^{2}{y}^{2} + 25y^{4}$

f)

${( 3{x}^{2} - 4{y}^{2} )}^{2} = (3 {x}^{2} )^{2} - 2 \cdot (3{x}^{2}) \cdot (4{y}^{2}) + ( 4{y}^{2} )^{2} = 9x^{4} - 24{x}^{2}{y}^{2} + 16y^{4}$