Question

Descompuneti in factori aplicand formula a^2-b^2=(a+b)(a-b)
a)(x-2)^2-3^2
b)(x+1)^2-4^2
c)(2x+3)^2-4
d)(x-1)^2-4^2
e)(3a+b)^2-a^2
f)(7m+n)^2-4n^2
g)(x+y+1)^2-x^2
h)(3x+4y)^2-49a^2
i)(x^2+1)^2-x^4

Answer 1

a)(x-2)^2-3^2=(x-2-3)(x-2+3)=(x-5)(x+1)

b)(x+1)^2-4^2=(x+1-4)(x+1+4)=(x-3)(x+5)

c)(2x+3)^2-4=(2x+3-2)(2x+3+2)=(2x+1)(2x+5)

d)(x-1)^2-4^2=(x-1-4)(x-1+4)=(x-5)(x+3)

e)(3a+b)^2-a^2=(3a+b-a)(3a+b+a)=(2a+b)(4a+b)

f)(7m+n)^2-4n^2=(7m+n-4n)(7m+n+4n)=(7m-3n)(7m+5n)

g)(x+y+1)^2-x^2=(x+y+1-x)(x+y+1+x)=(y+1)(2x+y+1)

h)(3x+4y)^2-49a^2=(3x+4y-7a)(3x+4y+7a)

i)(x^2+1)^2-x^4=(x^2+1-x^2)(x^2+1+x^2)=2x^2+1