Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (-2x-3y)(3x+2y)

Bergen 2021-09-12 Answered
Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
\(\displaystyle{\left(-{2}{x}-{3}{y}\right)}{\left({3}{x}+{2}{y}\right)}\)

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Expert Answer

StrycharzT
Answered 2021-09-13 Author has 22854 answers
FOIL method is first, outer, inner, last.
The given polynomial is,
\(\displaystyle{\left(-{2}{x}-{3}{y}\right)}{\left({3}{x}+{2}{y}\right)}\)
Opening the bracket to solve the equation as,
\(\displaystyle{\left(-{2}{x}-{3}{y}\right)}{\left({3}{x}+{2}{y}\right)}=-{2}{x}\times{3}{x}-{2}{x}\times{2}{y}-{3}{y}\times{3}{x}-{3}{y}\times{2}{y}\)
\(\displaystyle=-{6}{x}^{{2}}-{4}{x}{y}-{9}{x}{y}-{6}{y}^{{2}}\)
After separating the terms, the final product of the polynomials will be,
\(\displaystyle{\left(-{2}{x}-{3}{y}\right)}{\left({3}{x}+{2}{y}\right)}=-{6}{x}^{{2}}-{12}{x}{y}-{6}{y}^{{2}}\)
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