Question

Descompune:
a) x²-x²y+xy²-y³

b) x²+ ax + bx +ab

c) xy +5x+ 3y + 15

d) a²b²- 16c²

e)2a²-3

f) 81-c²

g ) 64 x⁴- y⁴

h) x²- y²+ √2x+ √2y

i) 7x-7y+ 4x²- 4y²

j)a²- b²+ 1/2a- 1/2b

Answer 1

a) x²-x²y+xy²-y³=x²(1-y)+y²(x-y) ???
ar fi trebuit: 
x³-x²y+xy²-y³=x²(x-y)+y²(x-y)=(x-y)(x²+y²)

b) x²+ ax + bx +ab=x(x+a)+b(x+a) =(x+a)(x+b)

c) xy +5x+ 3y + 15=x(y+5)+3(y+5)=(y+5)(x+3)

d) a²b²- 16c² =(ab-4c)(ab+4c)

e)2a²-3 =(a√2-√3)(a√2+√3)

f) 81-c² =(9+x)(9-x)

g ) 64 x⁴- y⁴=(8x²-y²)(8x²+y²)=(2√3x-y)(2√3x+y)(8x²+y²)

h) x²- y²+ √2x+ √2y=(x+y)(x-y)+√2(x+y)=(x+y)(x-y+√2

i) 7x-7y+ 4x²- 4y²=7(x-y)+4(x+y)(x-y)=(x-y)(7+4x+4y)

j)a²- b²+ 1/2a- 1/2b= (a+b)(a-b)+1/2(a-b) =(a-b)(a+b+1/2)