Question

descompuneti in factori
a)$(3x+1) ^{2} -(4x+3) ^{2}$'
b)$(2a+7b) ^{2} -(3a-5b) ^{2}$
c)$(a+b+c) ^{2} -(a-b-c) ^{2}$
d)$(x+y-a) ^{2} -(x-y-a) ^{2}$
e)$x^{2n} -9$
f)$x^{2n} -y ^{2n}$

Answer 1

(3x+1)²-(4x+3)² = (3x+1+4x+3)(3x+1-4x-3)=(7x+4)(-x-2)

(2a+7b)²-(3a-5b)²=(2a+7b+3a-5b)(2a+7b-3a+5b)=(5a-2b)(-a+12b)

(a+b+c)²-(a-b-c)²=(a+b+c+a-b-c)(a+b+c-a+b+c)=2a(2b+2c)=4a(b+c)
(x+y-a)²-(x-y-a)²=(x+y-a+x-y-a)(x+y-a-x+y+a)=(2x-2a)(2y)=4y(x-a)

x^2n-9= (x^n+3)(x^n-3)

x^2n-y^2n= (x^n+y^n)(x^n-y^n)