For F(x, y) = 4x^2 - 5xy, what is F(λ x, λ y)?

Question 8

EasyOriginal question

For $F(x, y) = 4x^{2} - 5xy$ , what is $F(\lambda x, \lambda y)$ ?

\lambda(4x^{2} - 5xy)

Correct answerYour answer

4\lambda^{2}x^{2} - 5\lambda xy

Correct answerYour answer

4\lambda x^{2} - 5\lambda^{2}xy

Correct answerYour answer

\lambda^{2}(4x^{2} - 5xy)

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Replace $x$ by $\lambda x$ and $y$ by $\lambda y$ : $4\lambda^{2}x^{2} - 5(\lambda x)(\lambda y)$ .
Both terms carry $\lambda^{2}$ , so $F(\lambda x, \lambda y) = \lambda^{2}(4x^{2} - 5xy)$ : degree 2.

Worth noting

$\lambda(4x^{2} - 5xy)$ brings in one $\lambda$ ; each of the two letters in $x^{2}$ and in $xy$ brings its own.

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