# To multiply: the given binomial using FOIL method. 5x^{2}(3x^{2

To multiply: the given binomial using FOIL method.
$$\displaystyle{5}{x}^{{{2}}}{\left({3}{x}^{{{2}}}-{x}+{2}\right)}$$

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Annie Midgett
Step 1
The given equation is
$$\displaystyle{5}{x}^{{{2}}}{\left({3}{x}-{x}+{2}\right)}$$
Now, multiply the given trinomial by applying distributive property,
$$\displaystyle{5}{x}^{{{2}}}{\left({3}{x}^{{{2}}}-{x}+{2}\right)}$$
$$\displaystyle={\left({\left({3}{x}^{{{2}}}\right)}{\left({5}{x}^{{{2}}}\right)}-{\left({x}\right)}{\left({5}{x}^{{{2}}}\right)}+{\left({2}\right)}{\left({5}{x}^{{{2}}}\right)}\right)}$$
$$\displaystyle{5}{x}^{{{2}}}{\left({3}{x}^{{{2}}}-{x}+{2}\right)}$$
$$\displaystyle={\left({15}{x}^{{{4}}}-{5}{x}^{{{3}}}+{10}{x}^{{{2}}}\right)}$$
$$\displaystyle{5}{x}^{{{2}}}{\left({3}{x}^{{{2}}}-{x}+{2}\right)}$$
$$\displaystyle={15}{x}^{{{4}}}-{5}{x}^{{{3}}}+{10}{x}^{{{2}}}$$
Hence, the multiplication of the given expression is
$$\displaystyle{5}{x}^{{{2}}}{\left({3}{x}^{{{2}}}-{x}+{2}\right)}={15}{x}^{{{4}}}-{5}{x}^{{{3}}}+{10}{x}^{{{2}}}$$