What must be added to $81 x^{2} - 72 x + 9$ $81x^2 - 72x + 9$ to make it a perfect square?

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What must be added to $81 x^{2} - 72 x + 9$ $81x^2 - 72x + 9$ to make it a perfect square?

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Answer 1 · 2016-03-31T22:01:04

A constant solution would be $7$ $7$

Another solution is $18 x$ $18x$

Explanation:

$81 x^{2} - 72 x + 9 + 7 = 81 x^{2} - 72 x + 16 = {(9 x - 4)}^{2}$ $81x^2-72x+9+7 = 81x^2-72x+16 = (9x-4)^2$

$81 x^{2} - 72 x + 9 + 18 x = 81 x^{2} - 54 x + 9 = {(9 x - 3)}^{2}$ $81x^2-72x+9+18x = 81x^2-54x+9 = (9x-3)^2$

In general,

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ $(a-b)^2 = a^2-2ab+b^2$

In the above solutions, we choose to change the constant term to match the $- 2 a b$ $-2ab$ term or the $- 2 a b$ $-2ab$ term to match the $b^{2}$ $b^2$ term.

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What must be added to $81 x^{2} - 72 x + 9$ $81x^2 - 72x + 9$ to make it a perfect square?

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Explanation:

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What must be added to 81x^2 - 72x + 981x2−72x+981x^2 - 72x + 9 to make it a perfect square?

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Explanation:

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What must be added to $81 x^{2} - 72 x + 9$ $81x^2 - 72x + 9$ to make it a perfect square?