Question

substitua cada polinômio a seguir por um produto:

a)a²-256=

b)x²-x+¼ =

c)4x²-x+1/16=

d)x²-y⁸=​

Answer 1

Explicação passo-a-passo:

a) $a^2-256=a^2-16^2$

$a^2-256=(a-16)\cdot(a+16)$

b) $x^2-x+\dfrac{1}{4}=x^2-2\cdot x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2$

$x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)^2$

$x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)\cdot\left(x-\dfrac{1}{2}\right)$

c) $4x^2-x+\dfrac{1}{16}=(2x)^2-2\cdot2x\cdot\dfrac{1}{4}+\left(\dfrac{1}{4}\right)^2$

$4x^2-x+\dfrac{1}{16}=\left(2x-\dfrac{1}{4}\right)^2$

$4x^2-x+\dfrac{1}{16}=\left(2x-\dfrac{1}{4}\right)\cdot\left(2x-\dfrac{1}{4}\right)$

d) $x^2-y^8=x^2-(y^4)^2$

$x^2-y^8=(x-y^4)\cdot(x+y^4)$