Răspuns :
[tex]a)9 {(x + 2)}^{2} - 4 {(3x - 7)}^{2} [/tex]
[tex] = 9( {x}^{2} + 4x + 4) - 4(9 {x}^{2} - 42x + 49)[/tex]
[tex] = 9 {x}^{2} + 36x + 36 - 36 {x}^{2} + 168x - 196 [/tex]
[tex] = - 27 {x}^{2} + 204x - 160[/tex]
[tex]c)36 {x}^{2} - {( {x}^{2} - 2x + 3)}^{2} [/tex]
[tex] = 36 {x}^{2} - ( {x}^{4} + 4 {x}^{2} + 9 -4{x}^{3} + 12x + 6 {x}^{2} ) [/tex]
[tex] = 36 {x}^{2} - {x}^{4} - 4 {x}^{2} - 9 +4 {x}^{3} -12x - 6 {x}^{2} [/tex]
[tex] = - {x}^{4} +4 {x}^{3} + 26 {x}^{2} - 12x - 9[/tex]
[tex] = 9( {x}^{2} + 4x + 4) - 4(9 {x}^{2} - 42x + 49)[/tex]
[tex] = 9 {x}^{2} + 36x + 36 - 36 {x}^{2} + 168x - 196 [/tex]
[tex] = - 27 {x}^{2} + 204x - 160[/tex]
[tex]c)36 {x}^{2} - {( {x}^{2} - 2x + 3)}^{2} [/tex]
[tex] = 36 {x}^{2} - ( {x}^{4} + 4 {x}^{2} + 9 -4{x}^{3} + 12x + 6 {x}^{2} ) [/tex]
[tex] = 36 {x}^{2} - {x}^{4} - 4 {x}^{2} - 9 +4 {x}^{3} -12x - 6 {x}^{2} [/tex]
[tex] = - {x}^{4} +4 {x}^{3} + 26 {x}^{2} - 12x - 9[/tex]
a) aplicam formula (a-b)² = a²-2ab+b² si (a+b)²=a²+2ab+b²
9(x²+4x+4)-4(9x²-42x+49) =9x²+36x+36-36x²+168x-196 = -26x²+204x-160
c) 36x²-(x^4 +4x²+9 -2·x²·(-2x)+2·x²·3-2·(-2x)·3) = 36x²-x^4 +4x³-10x²+12x-9 = -x^4+4x³+26x²+12x-9
Am aplicat formula (a-b+c)² = a²+b²+c²-2ab+2ac-2bc.