Построить график функциипроизводнаяy=3x^3 -x+2с решением

Пошаговое объяснение:

1) 16x4 - 81=(4Х^2)^2-9^2=(4Х^2+9)(4Х^2-9)=(4Х^2+9)(2х+3)(2х-3)

б) х^2 - у^2 - 14у- 49=х^2-(у^2+2*7*у+7^2)=х^2-(у+7)^2=(х+у+7)(х-(у+7))=(х+у+7)(х-у-7)

в) a^3 + a^2b - ab^2 - b^3=(a^3 + a^2b) - (ab^2 + b^3) =а^2(а+b)-b^2(a+b)=(a+b)(a^2-b^2)=(a+b)(a+b)(a-b)=(a+b)^2(a-b)

5. Решите уравнение:

у^3 + 3y^2 - у - 3 = 0

(у^3 + 3y^2) - (у +3) = 0

y^2(y+3)-(y+3)=0

(y+3)(y^2-1)=0

(y+3)(y+1)(y-1)=0

у1=-3, у2=-1, у3=1

6. Докажите тождество: (x + 2y)^2 - (x - 2y)^2 = 8xy

Преобразуем левую часть тождества:

(x + 2y)^2 - (x - 2y)^2 = х^2+4ху+4у^2-х^2+4ху-у^2=8ху, ч. т. д

7.Чему равно 2a^2 - 4ab + 2b^2 , если a-b=7?

2a^2 - 4ab + 2b^2=2( a^2 - 2ab + b^2) =2(а-b)^2=2*7^2=2*49=98

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