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Addition and Subtraction of Algebraic Expression

What should b...

Question

What should be added to $x y - 3 y z + 4 z x$ to get $4 x y - 3 z x + 4 y z + 7$ ?

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Solution

Let, the polynomial that should be added be $P$ .

Then according to question,
$(x y - 3 y z + 4 z x) + P = (4 x y - 3 z x + 4 y z + 7) \Rightarrow P = (4 x y - 3 z x + 4 y z + 7) - (x y - 3 y z + 4 z x) \Rightarrow P = 4 x y - 3 z x + 4 y z + 7 - x y + 3 y z - 4 z x$

Rearranging and collecting like terms,
$P = 4 x y - x y - 3 z x - 4 z x + 4 y z + 3 y z + 7 \Rightarrow P = 3 x y - 7 z x + 7 y z + 7$

Hence, $3 x y - 7 z x + 7 y z + 7$ should be added to get the required result.

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