Question

descompuneți in factori:
a) (x+1)(x+3)²-4(x+1)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
VA ROG URGENT PUNCTELE E, F, G, H, I, J, K, L, M !!!!
​

Answer 1

Răspuns:

Explicație pas cu pas:

a) (x+1)(x+3)²-4(x+1) = (x+1)(x²+6x+9-4) = (x+1)(x²+6x+5)=

=(x+1)(x²+5x+x+5) = (x+1)·[x(x+5)+(x+5)] = (x+1)(x+5)(x+1) = (x+1)²·(x+5)

----------------

b) (x+3)(2x+1)²-16(x+3) = (x+3)[(2x+1)²-16] = (x+3)(2x+1-4)(2x+1+4) =

=(x+3)(2x-3)(2x+5)

---------------

c) (x-3)(x+2)²-x+3 = (x-3)[(x+2)²-1²] = (x-3)(x+2-1)(x+2+1) =

= (x-3)(x+1)(x+3)

----------------

d) (x-4)(2x+1)²-x+4 = (x-4)[(2x+1)²-1²] = (x-4)(2x+1-1)(2x+1+1) =

= (x-4)(2x+2)·2x = 4x(x-4)(x+1)

----------------

e) (x+8)²-25 = (x+8-5)(x+8+5) = (x+3)(x+13)

---------------

f) (2x-5)²-36 = (2x-5-6)(2x-5+6) = (2x-11)(2x+1)

----------------

g) (x-5)²-9x² = (x-5)²-(3x)² = (x-5-3x)(x-5+3x) = (-2x-5)(4x-5) = (2x+5)(5-4x)

---------------

h) (2x+5)²-(x+3)² = (2x+5-x-3)(2x+5+x+3) = (x+2)(3x+8)

---------------

i) (3x+4)²-(x+5)² = (3x+4-x-5)(3x+4+x+5) = (2x-1)(4x+9)

---------------

j) (2x+1)²-(x-1)² = (2x+1-x+1)(2x+1+x-1) = (x+2)·3x

---------------

k) (3x+2)²-(2x+1)² = (3x+2-2x-1)(3x+2+2x+1) = (x+1)(5x+3)

----------------

l) (3x-1)²-4(x+1)² = (3x-1)²-(2x+2)² = (3x-1-2x-2)(3x-1+2x+2) =

= (x-3)(5x+1)

-------------------

m) (4x-3)²-9(x+2)² = (4x-3)²-(3x+6)² = (4x-3-3x-6)(4x-3+3x+6) =

= (x-9)(7x+3)

Am folosit formula : a²-b² = (a-b)(a+b)