Question

Ofer coroana celui mai bun și corect răspuns!!​

Answer 1

Explicație pas cu pas:

a)

${x}^{2} + 6x + 9 = {x}^{2} + 2 \times 3x + {3}^{2} = {(x + 3)}^{2}$

b)

${x}^{2} - 6x + 9 = {x}^{2} - 2 \times 3x + {3}^{2} = {(x - 3)}^{2}$

c)

$4 {x}^{2} + 12x + 9 = {(2x)}^{2} + 2 \times 2x \times 3x \times {3}^{2} = {(2x + 3)}^{2}$

d)

$4 {x}^{2} - 12x + 9 = {(2x)}^{2} - 2 \times 2x \times 3x \times {3}^{2} = {(2x - 3)}^{2}$

e)

$4 {x}^{2} - 25 = {(2x)}^{2} - {5}^{2} = (2x - 5)(2x + 5)$

f)

$25 {x}^{4} - 4 = {(5 {x}^{2} )}^{2} - {2}^{2} = (5 {x}^{2} - 2)(5 {x}^{2} + 2) = ({( \sqrt{5} x)}^{2} - {( \sqrt{2} )}^{2} )(5 {x}^{2} + 2) = ( \sqrt{5}x - \sqrt{2})( \sqrt{5}x + \sqrt{2})(5 {x}^{2} + 2)$

g)

${x}^{4} - 18 {x}^{2} + 81 = {( {x}^{2} )}^{2} - 2 \times {x}^{2} \times 9 + {9}^{2} = {( {x}^{2} - 9)}^{2} = {( {x}^{2} - {3}^{2} )}^{2} = {[(x - 3)(x + 3)]}^{2} = {(x - 3)}^{2} {(x + 3)}^{2}$

h)

${x}^{4} + 10 {x}^{2} + 25 = {( {x}^{2} )}^{2} + 2 \times {x}^{2} \times 5 + {5}^{2} = {( {x}^{2} + 5)}^{2}$