Sabrina Waller

2022-01-31

What is the standard form of $y=(-7x-{x}^{2})(x+3)-{(x-12)}^{3}$ ?

Dylan Trevino

Beginner2022-02-01Added 7 answers

Explanation:

Given:

$y=(-7x-{x}^{2})(x+3)-{(x-12)}^{3}$

Expanding rhs and simplifying

$y=-7{x}^{2}-{x}^{3}-21x-3{x}^{2}-({x}^{3}-3\times 12{x}^{2}+3\times {12}^{2}x-{12}^{3})$

$y=-7{x}^{2}-{x}^{3}-21x-3{x}^{2}-{x}^{3}+3\times 12{x}^{2}-3\times 144x+1728)$

$y=(-1-1){x}^{3}+(-7-3+36){x}^{2}+(-21-432)x+1728$

$y=-2{x}^{3}+26{x}^{2}-453x+1728$

Answer:

$y=-2{x}^{3}+26{x}^{2}-453x+1728$

happens to be the standard form

$y=a{x}^{3}+b{x}^{2}+cx+d$

Given:

Expanding rhs and simplifying

Answer:

happens to be the standard form

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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