Question

hcf of the termof the expression4p^3q^2r-12pq^2r^2+16p^2q^2r^2​

Answer 1

SOLUTION

TO DETERMINE

The HCF of the term of the expression

$\sf{4 {p}^{3} {q}^{2} r - 12p {q}^{2} {r}^{2} + 16 {p}^{2} {q}^{2} {r}^{2} }$

EVALUATION

Here the given expression is

$\sf{4 {p}^{3} {q}^{2} r - 12p {q}^{2} {r}^{2} + 16 {p}^{2} {q}^{2} {r}^{2} }$

So the terms are

$\sf{4 {p}^{3} {q}^{2} r \: , \: 12p {q}^{2} {r}^{2} \: ,\: 16 {p}^{2} {q}^{2} {r}^{2} }$

Now

$\sf{4 {p}^{3} {q}^{2} r = 2 \times 2 \times p \times p \times p \times q \times q \times r\: }$

$\sf{12p {q}^{2} {r}^{2} = 2 \times 2 \times 3 \times p \times q \times q \times r \times r \: }$

$\sf{ 16 {p}^{2} {q}^{2} {r}^{2} = 2 \times 2\times 2 \times 2\times p \times p \times q \times q \times r \times r}$

Hence HCF

$\sf{ = 4p {q}^{2} r\: }$

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