find the LCM of 10(9x²+6xy+y²),12(3x²-5xy-2y²),14(6x⁴+2x³)
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0
Answer:
10(9x
2
+6xy+y
2
)
=10[(3x)
2
+(2×3x×y)+y
2
)]
=10[(3x+y)
2
](∵(a+b)
2
=a
2
+b
2
+2ab)
=2×5×(3x+y)×(3x+y)
12(3x
2
−5xy−2y
2
)
=12(3x
2
−6xy+xy−2y
2
)
=12[3x(x−2y)+y(x−2y)]
=12(3x+y)(x−2y)
=2×2×3×(3x+y)×(x−2y)
14(6x
4
+2x
3
)
=14×2x
3
(3x+1)
=28x
3
(3x+1)
=2×2×7×x×x×x×(3x+1)
Now multiply all the factors, using each common factor only once, therefore, the LCM is:
2×2×3×5×7×x×x×x×(3x+y)×(3x+y)×(x−2y)×(3x+1)=420x
3
(3x+y)
2
(x−2y)(3x+1)
Hence, the LCM of 10(9x
2
+6xy+y
2
),12(3x
2
−5xy−2y
2
) and 14(6x
4
+2x
3
) is 420x
3
(3x+y)
2
(x−2y)(3x+1).
Answered by
0
10(9x2+6xy+y 2[1254=9.523
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