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What is the standard form of # y= (5x+3)^3+(7x-13)^2#?

Answer 1

Eva Adamson

#(5x+3)^3+(7x-13)^2 = 125x^3+274x^2-47x+196#

In general we have:

#(a+b)^2 = a^2+2ab+b^2#

#(a+b)^3 = a^3+3a^2b+3ab^2+b^3#

So:

#(7x-13)^2 = (7x)^2-2(7x)(13)+13^2#

#color(white)((7x-13)^2) = 49x^2-182x+169#

#(5x+3)^3 = (5x)^3+3(5x)^2(3)+3(5x)(3^2)+3^3#

#color(white)((5x+3)^3) = 125x^3+225x^2+135x+27#

So:

#(5x+3)^3+(7x-13)^2#

#= 125x^3+225x^2+135x+27 + 49x^2-182x+169#

#= 125x^3+(225+49)x^2+(135-182)x+(27+169)#

#= 125x^3+274x^2-47x+196#

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Answer 2

Hazel Anglin

The standard form of the given equation ( y = (5x + 3)^3 + (7x - 13)^2 ) is:

[ y = 125x^3 + 375x^2 + 351x + 1329 ]

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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.