Question

Given P(x)=3x^2+4y^2 and R(x)=-7x^2+4xy-3y^2, find P(x)-R(x)

Polynomials
ANSWERED
asked 2021-09-19

Given \(\displaystyle{P}{\left({x}\right)}={3}{x}^{{2}}+{4}{y}^{{2}}\) and \(\displaystyle{R}{\left({x}\right)}=-{7}{x}^{{2}}+{4}{x}{y}-{3}{y}^{{2}}\), find \(P(x)-R(x)\).

Expert Answers (1)

2021-09-20
The given polynomials are:
\(\displaystyle{P}{\left({x}\right)}={3}{x}^{{2}}+{4}{y}^{{2}}\)
\(\displaystyle{R}{\left({x}\right)}=-{7}{x}^{{2}}+{4}{x}{y}-{3}{y}^{{2}}\)
Now the difference between the both polynomials is:
\(\displaystyle{P}{\left({x}\right)}-{R}{\left({x}\right)}={\left({3}{x}^{{2}}+{4}{y}^{{2}}\right)}-{\left(-{7}{x}^{{2}}+{4}{x}{y}-{3}{y}^{{2}}\right)}\)
\(\displaystyle{P}{\left({x}\right)}-{R}{\left({x}\right)}={3}{x}^{{2}}+{4}{y}^{{2}}+{7}{x}^{{2}}-{4}{x}{y}+{3}{y}^{{2}}\)
\(\displaystyle{P}{\left({x}\right)}-{R}{\left({x}\right)}={\left({3}{x}^{{2}}+{7}{x}^{{2}}\right)}-{4}{x}{y}+{\left({4}{y}^{{2}}+{3}{y}^{{2}}\right)}\)
\(\displaystyle{P}{\left({x}\right)}-{R}{\left({x}\right)}={10}{x}^{{2}}-{4}{x}{y}+{7}{y}^{{2}}\)
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