Question

Fatore os seguintes trinômios quadrados perfeitos:
A) x⁴-12x²+36

B) 9x²-24xy+16y²​

Answer 1

a)

$\mathsf{{x}^{4}-12{x}^{2}+36}\\\mathsf{\sqrt{{x}^{4}}={x}^{2}}\\\mathsf{\sqrt{36}=6}\\\mathsf{{x}^{4}-12{x}^{2}+36={({x}^{2}-6)}^{2}}$

b)

$\mathsf{9{x}^{2}-24xy+16{y}^{2}}\\\mathsf{\sqrt{9{x}^{2}}=3x~~\sqrt{16{y}^{2}}=4y}\\\mathsf{9{x}^{2}-24xy+16{y}^{2}={(3x-4y)}^{2}}$

Answer 2

Oie, Td Bom?!

A)

$x {}^{4} - 12x {}^{2} + 36$

$x {}^{2*2} - 2*x {}^{2} *6 + 6 {}^{2}$

$(x {}^{2} ) {}^{2} - 2*x {}^{2} *6 + 6 {}^{2}$

$( {x}^{2} - 6) {}^{2}$

B)

$9x {}^{2} - 24xy + 16y {}^{2}$

$3 {}^{2} x {}^{2} - 2*3x*4y + 4 {}^{2} y {}^{2}$

$(3x) {}^{2} - 2*3x*4y + (4y) {}^{2}$

$(3x - 4y) {}^{2}$

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