Question

a)a↑2-10a+25 b)9a↑2+6a+1 c)25x↑2-20x+4 d)9x↑2-6x+1 e)a↑4+8a↑2+16

Answer 1

Boa noite Enoque

a) a² - 10a + 25 = (a - 5)²

b) 9a² + 6a + 1  = (3a + 1)² 

c) 25x² - 20x + 4 = (5x + 2)²

d) 9x² - 6x + 1 = (3x + 1)²

e) a⁴ + 8a² + 16 = (a² + 4)² 

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Answer 2

Oie, Td Bom?!

a)

$= a {}^{2} - 10a + 25$

$= a {}^{2} - 2 \: . \: a \: . \: 5 + 5 {}^{2}$

$= (a - 5) {}^{2}$

b)

$= 9a {}^{2} + 6a + 1$

$= 3 {}^{2} a {}^{2} + 2 \: . \: 3a \: . \: 1 + 1 {}^{2}$

$= (3a) {}^{2} + 2 \: . \: 3a \: . \: 1 + 1 {}^{2}$

$= (3a + 1) {}^{2}$

c)

$= 25x {}^{2} - 20x + 48$

$= 5 {}^{2} x {}^{2} - 2 \: . \: 5x \: . \: 2 + 2 {}^{2}$

$= (5x) {}^{2} - 2 \: . \: 5x \: . \: 2 + 2 {}^{2}$

$= (5x - 2) {}^{2}$

d)

$= 9x {}^{2} - 6x + 1$

$= 3 {}^{2} x {}^{2} - 2 \: . \: 3x \: . \: 1 + 1 {}^{2}$

$= (3x) {}^{2} - 2 \: . \: 3x \: . \: 1 + 1 {}^{2}$

$= (3x - 1) {}^{2}$

e)

$= a {}^{4} + 8a {}^{2} + 16$

$= a {}^{2 \: . \: 2} + 2 \: . \: a {}^{2} \: . \: 4 + 4 {}^{2}$

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

$= (a {}^{2} + 4) {}^{2}$

Att. Makaveli1996