Question

Descompune in factori : 
a.) x²+6×+9
b.) 4b²+9a²-12ab
c.) 5-2√5×+x²

Answer 1

Este formula:
$a^{2} +2*a*b+ b^{2} = (a+b)^{2}$
respectiv:
$a^{2} -2*a*b+ b^{2} = (a-b)^{2}$

a) $x^{2} +6*x+9$=
=$x^{2} +2*3*x+ 3^{2} =$
=$(x+3)^{2}$

b) $4* b^{2} + 9* a^{2} -12*a*b=$
=$(2* b)^{2} + (3* a)^{2} -2*(3*a)*(2*b)=$
=$(2*b-3*a)^{2}$

c) $5-2* \sqrt{5} *x+ x^{2} =$
= $( \sqrt{5} )^{2} -2* \sqrt{5} *x+ x^{2} =$
=$(\sqrt{5}-x)^{2}$