The standard form of #y = (x +1)^3 - (3x-2)^2#?

Answer 1

Savannah Anderson

Standard form is

#color(green)(y = x^3 - 6x^2 + 15x - 3)#

#y = (x+1)^3 - (3x-2)^2#

Expanding the terms

#y = (x^3 + 1 + 3x(x+1)) - (9x^2 + 4 - 12x)#

Removing the braces,

#y = x^3 + 1 + 3x^2 + 3x - 9x^2 - 4 + 12x##

Rearranging the like terms together and the polynomials in descending order to get the standard form

#y = x^3 + 3x^2 - 9x^2 + 3x + 12x + 1 - 4#

Combining the like terms and simplifying,

#color(green)(y = x^2 - 6x^2 + 15x - 3)#

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Answer 2

Jace Anderson

The standard form of the given expression ( y = (x + 1)^3 - (3x - 2)^2 ) is ( y = x^3 + 3x^2 + 3x - 1 - (9x^2 - 12x + 4) ), which simplifies to ( y = x^3 + 3x^2 + 3x - 1 - 9x^2 + 12x - 4 ). Combining like terms yields the standard form ( y = x^3 - 6x^2 + 15x - 5 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

The standard form of #y = (x +1)^3 ­- (3x-2)^2#?

The standard form of #y = (x +1)^3 - (3x-2)^2#?