1. Check the given equation `x^2+6x+9` is perfect square or not
Solution:
`x^2+6x+9`
Here `"F.T. = x^2, M.T. = 6x and L.T. = 9`
`(M.T.)^2 = (6x)^2 = 36x^2`
`4(F.T.)(L.T.) = 4 * x^2 * 9=36x^2`
`:. (M.T.)^2 = 4(F.T.)(L.T.)`
`:.` given polynomial is a perfect square.
2. Check the given equation `x^2-4xy+4y^2` is perfect square or not
Solution:
`x^2-4xy+4y^2`
Here `"F.T. = x^2, M.T. = -4xy and L.T. = 4y^2`
`(M.T.)^2 = (-4xy)^2 = 16x^2y^2`
`4(F.T.)(L.T.) = 4 * x^2 * 4y^2=16x^2y^2`
`:. (M.T.)^2 = 4(F.T.)(L.T.)`
`:.` given polynomial is a perfect square.
3. Check the given equation `4x^2+4x+4` is perfect square or not
Solution:
`4x^2+4x+4`
Here `"F.T. = 4x^2, M.T. = 4x and L.T. = 4`
`(M.T.)^2 = (4x)^2 = 16x^2`
`4(F.T.)(L.T.) = 4 * 4x^2 * 4=64x^2`
`:. (M.T.)^2 != 4(F.T.)(L.T.)`
`:.` given polynomial is not a perfect square.
4. Check the given equation `3x^2+5x+2` is perfect square or not
Solution:
`3x^2+5x+2`
Here `"F.T. = 3x^2, M.T. = 5x and L.T. = 2`
`(M.T.)^2 = (5x)^2 = 25x^2`
`4(F.T.)(L.T.) = 4 * 3x^2 * 2=24x^2`
`:. (M.T.)^2 != 4(F.T.)(L.T.)`
`:.` given polynomial is not a perfect square.
This material is intended as a summary. Use your textbook for detail explanation.
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