Calculo

Calculo

Simplifique as expressões:

a)(x-4) (3x-1) = 3x²-x-12x+4=3x²-12x+4

b)(a-1) (a+1) = a²-1

c)-5(1/2 x- 1/3) (-2x+3) =

d)(2x- 1/2)² =

Efetue os quadrados dos binômios:

a)(3x+1)² =(3x)²+2.3x.1+1² =

=9x²+6x+1

b)(2m+5)² =(2m)²+2.2m.5+5²=

=4m²+20m+25

c)(5ab-7)² =(5ab)²-2.5ab.7+7²=

= 25a²b²-70ab+49

d)(11a²b³+7)² =(11a²b³)+2.11ª²b³.7+7²=

= 121ab+154a²b³+49

e)(x² - x³ )²=(x² )²-2.x² .x³ +(x³ )²=

= x -2x +x

f)(2x³-3y²)² =(2x³)² -2.2x³.3y²+(3y²)²=

= 4x -12x³y²+9y

g)(-t+8)²= (-t)²-2.t.8+8²=

= t²-16t+64

h)(-mp-2)²=(-mp)²-2.(-mp).2+2²=

= m²p²+4mp+4

i)(x/y-y/x)² =(x/y)²-2.(x/y.y/x)+(y/x)²=

= x²/y²- 2y²/x²

j)(3x/y-y/x)² =(3x/y)²+2.3x/y.2y/x+(2y/x)²=

= 9x²/y²+12+4y²/x²

Efetue os produtos:

a)(2x+1).(2x-1)= (2x)²-(1)²= 4x²-1

b)(3x²-4).(3x²+4)= (3x)²-(4)²= 9x-16

c)(6ab+1).(6ab-1)= (6ab)²-1²= 36a²b²-1

d)(m²+p³).(m²-p³)= (m²)²-(p³)²= m – p

e)(5x³+2).(2-5x³)= (5x³)²-(2)²= 25x -4

f)(x –x ).(x +x )= (x )²-(x )²=x² -x

g)(2p/3+3m/4).(2p/3-3m/4)=(2p/3)²-(3m/4)²=4p²/9- 9m²/16

Efetue os cubos dos binômios:

a)(3x+2)³=

b)(m+5)³=

c)(5ab-1)³=

d)(4x²-3y)³=

e)(a²b³+2)³=

f)(m² -p³ )³=

Efetue:

a)(x+2y)²+(2x-y)²= (x²+4y)+(4x-y²)=4x-4y= x²y²

b)(2a-3b)²-(a-5b).(a+2b)= 3a²-9ab+19b²

c)(a+b+c)²=(a+b+c)²-(a²+b²+c²)=(a+b+c).(a+b+c)-(a²+b²+c²)

= (a²+ab+ac+ba+b²+bc)-(a²+b²+c²)

=a²+ab+ac+b²+bc

Esboce o gráfico :

a)f(x)=2x+3