Question

Simplify the expression to a polynomial in standard form: (x+5)(2x² + 2x - 3)

Answer 1

Answer:

$\sf \: 2x {}^{3} + 12x {}^{3} + 7x - 15$

Step-by-step explanation:

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Answer 2

Answer:

$2x^3 +12x^2 +7x -15$

Step-by-step explanation:

$\underline{\textbf{Standard form of a polymonial:}}\\\\\text{A polynomial whose terms are ordered from highest to lowest degree}.\\\\\text{For example,}\\\\x^2 +x +4\\\\x^3 +x^2 +x +3 \\\\\text{etc.}\\\\\underline{\textbf{Solution:}}\\\\\text{Given that,}\\\\~~~(x+5)(2x^2 +2x-3)\\\\=x(2x^2 +2x-3) +5(2x^2 +2x -3)~~~~~~~~~~~~~;\textbf{Distribute}\\\\=2x^3+2x^2 -3x+10x^2+10x -15~~~~~~~~~~~~~;\textbf{Multiply}\\\\=2x^3 +2x^2 +10x^2 +10x -3x-15~~~~~~~~~~~~~;\textbf{Rearrange}$

$=2x^3 +12x^2 +7x -15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Simplify}$

$\textbf{Hence the given product in standard form is}~2x^3 +12x^2 +7x -15.$