H.C.F. of the terms of the expression ( 4p³q²r – 12pq²r² + 16p²q²r² )
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Answer:
The HCF of the given expression =4pq^{2}=4pq
2
Step-by-step explanation:
We have,
4p^{3}q^{2}-12pq^2r^{2}+16p^{2}q^{2}r^{2}4p
3
q
2
−12pq
2
r
2
+16p
2
q
2
r
2
To find, HCF of the given expression = ?
∴ 4p^{3}q^{2}-12pq^2r^{2}+16p^{2}q^{2}r^{2}4p
3
q
2
−12pq
2
r
2
+16p
2
q
2
r
2
Taking 4 as common,
=4(p^{3}q^{2}-3pq^2r^{2}+4p^{2}q^{2}r^{2})=4(p
3
q
2
−3pq
2
r
2
+4p
2
q
2
r
2
)
Taking p as common,
=4p(p^{2}q^{2}-3q^2r^{2}+4pq^{2}r^{2})=4p(p
2
q
2
−3q
2
r
2
+4pq
2
r
2
)
Taking q^{2}q
2
as common,
=4pq^{2}(p^{2}-3r^{2}+4pr^{2})=4pq
2
(p
2
−3r
2
+4pr
2
)
The highest common factor of the expression = 4pq^{2}4pq
2
Hence, the HCF of the given expression =4pq^{2}=4pq
2
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