Find the HCF of: p2 + 4pq + 4q2 , p4 + 8pq3 and 3p4 - 10p2q2 + p3q
1 Answer
Solution:
Here, first expression
= \(p^2+4pq+4q^2\)
= \(p^2+2.p.2q+{(2q)}^2\)
= \({(p+2q)}^2\)
= (p+2q)(p+2q)
Second expression
= \(p^4+8pq^3\)
= \(p(p^3+8q^3)\)
= \(p(p^3+{(2q)}^3)\)
= \(p(p+2q)(p^2-2pq+4q^2)\)
Third expression
= \(3p^4+10p^2q^2+p^3q\)
= \(p^2(3p^2-10q^2+pq)\)
= \(p^2(3p^2+pq-10q^2)\)
= \(p^2(3p^2+(6-5)pq-10q^2)\)
= \(p^2(3p^2+6pq-5pq-10q^2)\)
= \(p^2(3p(p+2q)-5p(p+2q)\)
= \(p^2(p+2q)(3p-5q)\)
∴ HCF is (2+2q)
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