Question

Fatore por agrupamento:
a) ax – ay + bx – by =

b) 5ax – 5ay + bx – by =

c) x 2 + 5x + ax + 5a =

d) 6a 2 + 2ab – 3ac – bc =

e) t 3 + t 2 – 7t – 7 =

f) x 4 – x 3 – 9x + 9 =

g) 2b 2 + 2 – b 2 k – k =

h) bx 2 – 2by + 5x 2 – 10y =

i) a 5 + a 3 + 2a 2 + 2 =

j) cx + x + c + 1 =

Answer 1

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$\boxed{\begin{array}{l}\tt a)~\sf ax-ay+bx-by=a\cdot(x-y)+b\cdot(x-y)\\\sf=(a+b)\cdot(x-y)\\\tt b)~\sf 5ax-5ay+bx-by=5a(x-y)+b\cdot(x-y)\\\sf=(5a+b)\cdot(x-y)\\\tt c)~\sf x^2+5x+ax+5a=x\cdot(x+5)+a\cdot(x+5)\\\sf=(x+a)\cdot(x+5)\\\tt d)~\sf 6a^2+2ab-3ac-bc=2a(3a+b)-c(3a+b)\\\sf=(2a-c)\cdot(3a+b)\\\tt e)~\sf t^3+t^2-7t-7=t^2(t+1)-7\cdot(t+1)\\\sf=(t^2-7)\cdot(t+1)\end{array}}$

$\boxed{\begin{array}{l}\tt f)~\sf x^4-x^3-9x+9= x^3\cdot(x-1)-9\cdot(x-1)\\\sf=(x^3-9)\cdot(x-1)\\\tt g)~\sf2b^2+2-b^2k-k=2\cdot(b^2+1)-k\cdot(b^2+1)\\\sf(2-k)\cdot(b^2+1)\\\tt h)~\sf bx^2-2by+5x^2-10y=b\cdot(x^2-2y)+5\cdot(x^2-2y)\\\sf=(b+5)\cdot(x^2-2y)\\\tt i)~\sf a^5+a^3+2a^2+2=a^3\cdot(a^2+1)+2^\cdot(a^2+1)\\\sf=(a^3+2)\cdot(a^2+1)\\\tt j)~\sf cx+x+c+1=x\cdot(c+1)+1\cdot(c+1)\\\sf=(x+1)\cdot(c+1)\end{array}}$