Question

01) Calcule o resultado de cada quadrado da soma:
a) (b + 6)²

b) (2a + 2)²

c) (a + 2).(a + 2)

d) (2x + 10y)²

02) Faça o agrupamento dos monômios abaixo:

a) 6ax + 5bx – 12ax – 15bx + 4x =

b) 15y – 4z + 3x + 12y – 20z =

c) 22aw + 6x – 12aw – 6x =

03). Efetue
a) ( + 6x) + ( - 7x )=

b) ( - 3x) + (+ 12x)=

c) ( - 3y) + ( - 3y )=

d) (- 2m) + ( - m )=

e) ( -70 x) + (+ 14 x)=

f) ( + 8x) - ( - 3x)=

g) ( - 4y) - ( - y )=

h) ( - 5x) – ( - 11x)=

i) ( + 7y) - ( + 7y)=

04) Multiplique os monômios.

a) (+3x) . (- 4x)=

b) (-2x) . (+ 5x)=

c) ( - a) . (- 4a)=

d) (+3x) . (+5x)=

e) (-3a) . (- 7b)=

f) ( - 2x) . ( - 2xy)=

g) (3x) . (5y )=

h) (3ab) . (2a)=

Answer 1

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$\boxed{\underline{\sf Quadrado~da~soma~de~dois~termos}}\\\large\boxed{\boxed{\boxed{\boxed{\sf(a+b)^2=a^2+2ab+b^2}}}}$

1)

$\tt a)~\sf(b+6)^2=(b)^2+2\cdot b\cdot6+(6)^2\\\sf(b+6)^2=b^2+12b+36\checkmark\\\tt b)~\sf(2a+2)^2=(2a)^2+2\cdot2a\cdot2+(2)^2\\\sf(2a+2)^2=4a^2+8a+4\checkmark\\\tt c)~\sf(a+2)\cdot(a+2)=(a+2)^2\\\sf (a+2)^2=a^2+2\cdot a\cdot2+2^2\\\sf(a+2)^2=a^2+4a+4\checkmark\\\tt d)~\sf(2x+10y)^2=(2x)^2+2\cdot 2x\cdot10y+(10y)^2\\\sf (2x+10y)^2=4x^2+40xy+100y^2\checkmark$

2)

$\tt a)~\sf 6ax+5bx-12ax-15bx+4x=\\\sf-6ax-10bx+4x=2x\cdot(-3a-5b+2)\\\tt b)~\sf15y-4z+3x+12y-20z=3x+27y-24z=3\cdot(x+9y-8z)\\\tt c)~\sf 22aw+\diagup\!\!\!\!\!6x-12aw-\diagup\!\!\!\!\!\!6x=10aw\checkmark$

3)

$\tt a)~\sf(+6x)+(-7x)=6x-7x=-x\checkmark\\\tt b)~\sf(-3x)+(+12x)=-3x+12x=9x\checkmark\\\tt c)~\sf(-3y)+(-3y)=-3y-3y=-6y\checkmark\\\tt d)~\sf(-2m)+(-m)=-2m-m=-3m\checkmark\\\tt e)~\sf(-70x)+(+14x)=-70x+14x=-56x\checkmark\\\tt f)~\sf(+8x)-(-3x)=8x+3x=11x\checkmark\\\tt g)~\sf(-4y)-(-y)=-4y+y=-3y\checkmark\\\tt h)~\sf(-5x)-(-11x)=-5x+11x=6x\checkmark\\\tt i)~\sf(+7y)-(+7y)=\backslash\!\!\!\!7y-\backslash\!\!\!7y=0\checkmark$

4)

$\tt a)~\sf(+3x)\cdot(-4x)=-12x^2\checkmark\\\tt b)~\sf(-2x)\cdot(+5x)=-10x^2\checkmark\\\tt c)~\sf(-a)\cdot(-4a)=4a^2\checkmark\\\tt d)~\sf(+3x)\cdot(+5x)=15x^2\checkmark\\\tt e)~\sf(-3a)\cdot(-7b)=21ab\checkmark\\\tt f)~\sf(-2x)\cdot(-2xy)=4x^2y\checkmark\\\tt g)~\sf(3x)\cdot(5y)=15xy\checkmark\\\tt h)~\sf(3ab)\cdot(2a)=6a^2b\checkmark$