What is the HCF of $a^{2}$ $b^{3}$ $c^{2}$ , b $c^{3}$ , a $c^{2}$ ?

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$c^{3}$

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$b^{2}$

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$c^{2}$

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Solution

The correct option is D
$c^{2}$

All three terms are written as,

$a^{2}$ $b^{3}$ $c^{2}$ = a $\times$ a $\times$ b $\times$ b $\times$ b $\times$ c $\times$ c

b $c^{3}$ = b $\times$ c $\times$ c $\times$ c

And, a $c^{2}$ = a $\times$ c $\times$ c

We have $c^{2}$ common in all three terms/polynomials. So, the HCF for the given three polynomials is $c^{2}$ .

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In the given figure, ABCD is a rhombus. Then,

(a) $A C^{2} + B D^{2} = A B^{2}$

(b) $A C^{2} + B D^{2} = 2 A B^{2}$

(d) $2 (A C^{2} + B D^{2}) = 3 A B^{2}$

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