Find a monomial, which is added to $- 2 x + 4 y^{2} + z$ to make this expression a binomial.

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Solution

We can add $2 x, - 4 y^{2}$ and -z to the expression to make it binomial.
$\Rightarrow 2 x + (- 2 x + 4 y^{2} + z) = 4 y^{2} + z \Rightarrow - 4 y^{2} - (- 2 x + 4 y^{2} + z) = - 2 x + z \Rightarrow - z + (- 2 x + 4 y^{2} + z) = - 2 x + 4 y^{2}$
Hence, on adding a monomial $2 x$ or $- 4 y^{2}$ or $- z$ to $- 2 x + 4 y^{2} + z$ , the resulting expression becomes a binomal.

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