Algebraic Expressions and Identities — Maths STD 8 — Question
Maharashtra BoardEnglish MediumSTD 8MathsAlgebraic Expressions and Identities3 Marks
Question
What must be added to following expressions to make it a whole square?
$4 x^2-20 x+20$
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Answer
Let us consider the following expression: $4 x^2-20 x+20$
The above expression can be written as:
$4 x^2-20 x+20=(2 x)^2-2 \times 2 x \times 5+20$
It is evident that if $2 x$ is considered as the first term and 5 is considered as the second term, 5 is required to be added to the above expression to make it a perfect square. Therefore, number 20 must become 25 .
Therefore, adding and subtracting 5 in the above expression, we get:
$\left(4 x^2-20 x+20+5\right)-5$
$=\left\{(2 x)^2-2 \times 2 x \times 5+20\right\}+5-5$
$=\left\{(2 x)^2-2 \times 2 x \times 5+25\right\}-5$
$=(2 x+5)^2-5$
Thus, the answer is 5 .
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