Question

escreva a forma fatorada de cada um dos trinômios quadrados perfeitos a) 4a²-12ab+9b² b) 16xy+16x²+4y² c) 100-20ab+a²b²​

Answer 1

Oie, Td Bom?!

a)

$= 4a {}^{2} - 12ab + 9b {}^{2}$

$= 2 {}^{2} a {}^{2} - 2 \: . \: 2a \: . \: 3b + 3 {}^{2} b {}^{2}$

$= (2a) {}^{2} - 2 \: . \: 2a \: . \: 3b + (3b) {}^{2}$

$= (2a - 3b) {}^{2}$

b)

$= 16xy + 16x {}^{2} + 4y {}^{2}$

$= 4(4xy + 4x {}^{2} + y {}^{2} )$

$= 4(4x {}^{2} + 4xy + y {}^{2} )$

$= 4(2 {}^{2} x {}^{2} + 2 \: . \: 2x \: . \: y + y {}^{2} )$

$= 4((2x) {}^{2} + 2 \: . \: 2x \: . \: y + y {}^{2} )$

$= 4(2x + y) {}^{2}$

c)

$= 100 - 20ab + a {}^{2} b {}^{2}$

$= 10 {}^{2} - 2 \: . \: 10 \: . \: ab + (ab) {}^{2}$

$= (10 - ab) {}^{2}$

Att. Makaveli1996