Question

Fatore as expressões:
$A) 3x^5-18x^3=\\\\B) 5a^2+3ab+2a=\\\\C) 4x^2-25y^2=\\\\D) t^2-\frac{9}{64} \\\\E) x^2-11x+xy-11y=\\\\F)16x^2-56x+49=\\\\G)a^2+2ab^2+b^4=$

Answer 1

a) 3x⁵ - 18x³ ← fatorar 3

3(x⁵ - 6x³) ← fatorar x³

x³(x² - 6) ← reescreve a fatoração completa

3x³(x² - 6)

b) 5a² + 3ab + 2a ← fator a

a × (5a + 3b + 2)

c) 4x² - 25y² ← escrevendo na forma exponencial

2²x² - 5²y² ← multiplique bases e mantenha expoente

(2x)² - (5y)² ← usando a²-b²=(a-b)(a+b)

(2x - 5y) × (2x + 5y)

d) t² - 9/64 ← fatorar 1/64

64t²-9/64

(8t)²-3²/64 → a²-b²=(a-b)(a+b)

(8t-3)×(8t+3)/64

e) x² - 11x + xy - 11y ← fator x e y

x × (x - 11x) + y × (x - 11) ← fator x - 11

(x - 11) × (x + y)

f) 16x² - 56x + 49 ← forma exponencial

4²x² - 2 × 4x × 7 + 7² ← multiplica bases e mantenha expoente

(4x)² - 2 × 4x × 7 + 7² ← a²-2ab+b²=(a-b)²

(4x - 7)²

g) a² + 2ab² + b⁴ ← Fatorize o 4

a² + 2ab² + b²*² ← a^mn = (a^n)^m

a² + 2ab² + (b²)² ← a²+2ab+b²=(a+b)²

(a + b²)²

Answer 2

• A)

$\sf 3x^5\:-\:18x^3\\\\\\\sf propriedades\:dos\:expoentes:\quad \:a^{b+c}=a^ba^c\\\\\\\sf x^5=x^2x^3\\\\\\\sf 3x^2x^3-18x^3\\\\\\\sf 3x^2x^3-3\cdot \:6x^3\\\\\\\boxed{\sf S=\{ 3x^3\left(x^2-6\right) \}}$

• B)

$\sf 5a^2+3ab+2a\\\\\\\sf propriedades\:dos\:expoentes:\quad \:a^{b+c}=a^ba^c\\\\\\\sf a^2=aa\\\\\\\sf 5aa+3ab+2a\\\\\\\boxed{\sf S=\{ a\left(5a+3b+2\right)\}}$

• C)

$\sf 4x^2-25y^2\\\\\\\sf 4x^2-25y^2\Rightarrow\left(2x\right)^2-\left(5y\right)^2\\\\\\\sf \left(2x\right)^2-\left(5y\right)^2\\\\\\\sf {Aplique\:a\:regra\:da\:diferenca\:de\:quadrados:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)\\\\\\\sf \left(2x\right)^2-\left(5y\right)^2=\left(2x+5y\right)\left(2x-5y\right)\\\\\\\boxed{\sf S=\{ \left(2x+5y\right)\left(2x-5y\right)\}}$

• D)

$\sf t^2-\dfrac{9}{64} \\\\\\\sf \dfrac{64t^2-9}{64} \\\\\\\sf$

$\sf (8t-3)(8t+3)\\\\\\\boxed{\sf S=\{ \frac{(8t-3)(8t+3)}{64} \}}$

• E)

$\sf x^2-11x+xy-11y\\\\\\\sf \left(x^2-11x\right)+\left(xy-11y\right)\\\\\\\sf y\left(x-11\right)+x\left(x-11\right)\\\\\\\sf {Fatorar\:o\:termo\:comum\:}x-11\\\\\\\boxed{\sf \left(x-11\right)\left(x+y\right)}$

• F)

$\sf 16x^2-56x+49\\\\\\\sf \left(4x\right)^2-2\cdot \:4x\cdot \:7+7^2\\\\\\\sf {Aplique\:a\:f\acute{o}rmula\:do\:quadrado\:perfeito}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\\\\\\sf a=4x,\:b=7\\\\\\\boxed{\sf S=\{ \left(4x-7\right)^2\}}$

• G)

$\sf a^2+2ab^2+b^4\\\\\\\sf \left(a^2+ab^2\right)+\left(ab^2+b^4\right)\\\\\\\sf a\left(a+b^2\right)+b^2\left(a+b^2\right)\\\\\\\sf{Fatorar\:o\:termo\:comum\:}a+b^2\\\\\\\sf \left(a+b^2\right)\left(a+b^2\right)\\\\\\\boxed{\sf S=\{ \left(a+b^2\right)^2 \}}$