Question

1 ) Calculati, utilizand formula :
(a+b) ( a+b) = a² + b²
a ) ( 4 √5x-√15a)(4√5x+√15a)

2 ) Efectuati :
a) (a-2)(x+2)(x²+4)-(x²+1)²+2(x+1)
b) (x+4 ) (x²-3) -x² (x + 1)² + 2x(x-1)²

Answer 1

Prima formula nu este valida, deci trebuie sa-o aplicam pe cea corecta, adica: (a+b)(a-b)=a²-b²

1)a) $(4 \sqrt{5}x- \sqrt{15}a)(4 \sqrt{5}x+ \sqrt{15}a)=(4 \sqrt{5}x)^2 - ( \sqrt{15}a)^2= \\ =80x^2-15a^2$

2)a)$(a-2)(x+2)(x^2+4)-(x^2+1)^2+2(x+1)=ax^3+8a-16-2x^3-\\-(x^4+2x^2+1)+2x+2=ax^3+8a-16-2x^3-x^4-2x^2-1+2x\\+2=x^4+ax^3-2x^3-2x^2+8a+2x-15$
b)$(x+4)(x^2-3)-x^2(x+1)^2+2x(x-1)^2=(x^3-3x+4x^2-12)-\\-x^2(x^2+2x+1)+2x(x^2-2x+1)=x^3-3x+4x^2-12-x^4-2x^3\\-x^2+2x^3-4x^2+2x=-x^4+x^3-x-12$

Sfaturi:
-foloseste formulele invatate
-redu termenii asemenea
-scrie expresia de la cel mai mare numar pana la cel mai mic, sau cum vrei tu.

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