Question

Aplicati formula diferentelor de patrate si calculati:

a) (x+2)²-(x-2)² =

b) a²-(a-3)² =

c) 4a²-(2a-1)² =

d) (m²+m+1)²-(m²-m+1)² =

e) (a-b+c)²-(a+b+c)² =

f) (x+√2)²-8=

g) (√3y-1)²-243y² =

h) (x²+y²)²-4x²y² =

Answer 1

folosim relatia a²-b²=(a+b)(a-b)
a) (x+2)²-(x-2)²=(x+2+x-2)(x+2-x+2)=2x·4=6x
b) a²-(a-3)²=(a+a-3)(a-a+3)=3(2a-3)
c) 4a²-(2a-1)²=(2a+2a-1)(2a-2a+1)=4a-1
d) (m²+m+1)²-(m²-m+1)²=(m²+m+1+m²-m+1)(m²+m+1+m-m²+m-1)=(2m²+2)·2m=4m(m+1)
e) (a-b+c)²-(a+b+c)²=(a-b+c+a+b+c)(a-b+c-a-b-c)=(2a+2c)=2(a+c)
f) (x+√2)²-8=x²+2√2x+2-8=x²+2√2x-6
g) (√3y-1)²-243y²=3x²-2√3y+1-243y²=-240y²+2√3y+1
h) (x²+y²)²-4x²y²=x^4+y^4-2x²y²=(x²-y²)²