Question

Fatura por agrupamento

a) ax - mx + ay - my
b) a2 + ab + ac + bc
c) ax - bx + ay - by
d) ax + 2bx +3a +6b
e) xy + 2x - 2y - 4
f) 8x*2 +4xy + 2x + y
g) x3 - 5x*2 + 4x - 20
h) 2xy + x + 4y + 2

Answer 1

a) ax - mx + ay - my =   x(a - m) + y(a - m) = (x+y)(a-m)
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b) a2 + ab + ac + bc =  a(a + b) + c(a + b) = (a +b) (a+c)
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c) ax - bx + ay - by =   x(a - b) + y(a - b) = (x+y)(a-b)
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d) ax + 2bx +3a +6b =   x(a + 2b) + 3(a + 2b) = (x+3)(a+2b)
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e) xy + 2x - 2y - 4 =   x(y + 2) - 2(x + 2) = (x-2)(y+2)
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f) 8x*2 +4xy + 2x + y =  4x(2x + y) + 1(2x + y) = (2x+y)(4x+1)
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g) x3 - 5x*2 + 4x - 20 = x2(x - 5) + 4(x - 5) = (x2+4)(x-5)
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h) 2xy + x + 4y + 2 = x(2y+1) + 2(2y+1) ==> (x+2)(2y+1)