Answer:
Trinomial
[tex]m^2 - 13m + \frac{169}{4}[/tex]
Binomial squared
[tex](m - \frac{13}{2})^2[/tex]
Step-by-step explanation:
Given
[tex]m^2-13m[/tex]
Required
Make a perfect trinomial
We have:
[tex]m^2-13m =[/tex]
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Take the coefficient of m i.e. -13
Divide by 2 i.e. -13/2
Square i.e. (-13/2)
Add to both sides of the equation
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[tex]m^2-13m =[/tex] becomes
[tex]m^2 - 13m + (\frac{-13}{2})^2 = (\frac{-13}{2})^2[/tex]
[tex]m^2 - 13m + \frac{169}{4} = \frac{169}{4}[/tex]
Expand
[tex]m^2 - \frac{13}{2}m- \frac{13}{2}m + \frac{169}{4} = \frac{169}{4}[/tex]
Factorize:
[tex]m(m - \frac{13}{2})- \frac{13}{2}(m - \frac{13}{2}) = \frac{169}{4}[/tex]
Factor out m - 13/2
[tex](m - \frac{13}{2})(m - \frac{13}{2}) = \frac{169}{4}[/tex]
Write as square
[tex](m - \frac{13}{2})^2 = \frac{169}{4}[/tex]
Hence, the trinomial is:
[tex]m^2 - 13m + \frac{169}{4}[/tex]
And the binomial squared is:
[tex](m - \frac{13}{2})^2[/tex]
