Question

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

Answer 1

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

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.`

Answer 2

`\sf \: 2x {}^(3) + 12x {}^(3) + 7x - 15`

Explanation:

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