Respuesta :

Answer:

C) 64x2 + 40x + 25

Step-by-step explanation:

we are given

[tex]512x^3-125[/tex]

we can also write as

[tex]512=8^3[/tex]

[tex]125=5^3[/tex]

[tex]512x^3-125=(8x)^3-(5)^3[/tex]

we can use factor formula

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

we can compare and find 'a' and 'b'

a=8x

b=5

[tex]512x^3-125=(8x-5)((8x)^2+8x\times 5+(5)^2)[/tex]

now, we can simplify it

[tex]512x^3-125=(8x-5)(64x^2+40x+25)[/tex]

so, (64x^2+40x+25) factor matches

alinakincsem

Answer:

The correct answer option is  C) 64x^2 + 40x + 25.

Step-by-step explanation:

We are given the following expression:

[tex]512x^3 - 125[/tex]

which can also be written in the form of [tex]x^3-y^3[/tex] as:

[tex]\left(8x\right)^3-5^3[/tex]

Now we will apply the difference of cubes Formula:

[tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]

[tex](8x)^3-5^3=(8x-5)(8^2x^2+5*8x+5^2)[/tex]

[tex]=\left(8x-5\right)\left(8^2x^2+5\cdot \:8x+5^2\right)[/tex]

[tex]=\left(8x-5\right)\left(64x^2+40x+25\right)[/tex]

Therefore, from the given answer options we can see that the option C) 64x^2 + 40x + 25 is the factor of the given expression 512x^3 - 125.

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