Find and correct the errors (if any) in the following equations:

(i) $(5 x - 2)^{2} = 25 x^{2} + 4 - 20 x$

(ii) $(3 x + 2)^{2} = 3 x^{2} + 6 x + 4$

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Solution

Using the identities

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

(i) $(5 x - 2)^{2} = 25 x^{2} + 4 - 20 x$ is correct and there is no error.

(ii) $(3 x + 2)^{2} = 3 x^{2} + 6 x + 4$ is wrong .

The correct equation is
$(3 x + 2)^{2} = 9 x^{2} + 12 x + 4$ .

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Similar questions

Find and correct the errors (if any) in the following expressions:

$i .) (5 x - 2)^{2} = 25 x^{2} + 4 - 20 x$

$i i .) (3 x + 2)^{2} = 3 x^{2} + 6 x + 4$

Find and correct the errors (if any) in the following expressions:

$i .) (5 x - 2)^{2} = 25 x^{2} + 4 - 20 x$

$i i .) (3 x + 2)^{2} = 3 x^{2} + 6 x + 4$ [2 MARKS]

(3 x + 2)^{2} = 3 x^{2} + 6 x + 4

(3 x + 2)^{2} = 3 x^{2} + 6 x + 4

Find and correct the errors in the statement: (3x + 2)² = 3x² + 6x + 4

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