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Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.
Which product should Tomas choose?
A) (2x + 1)(2x2 + 2x – 1)
B) (2x + 1)(4x3 + 2x – 1)
C) (2x + 1)(4x2 – 2x + 1)
D) (2x + 1)(2x2 – 2x + 1)

Respuesta :

we know that

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

we are given

[tex] a=2x [/tex]

[tex] b=1 [/tex]

now, we can plug this in formula

and we get

[tex] (2x)^3+(1)^3=(2x+1)((2x)^2-(2x*1)+(1)^2) [/tex]

now, we can simplify it

and we get

[tex] (2x)^3+1^3=(2x+1)(4x^2-2x+1) [/tex]

so,

option-C.......Answer

mathecoach

(a + b) * (a^2 - a*b + b^2)

= (2x + (1)) * ((2x)^2 - (2x)*(1) + (1)^2)

C) (2x + 1) * (4x^2 - 2x + 1)

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