find the LCM of 10(9x²+6xy+y²),12(3x²-5xy-2y²),14(6x⁴+2x³)
Answers
Step-by-step explanation:
Least Common Multiple(LCM): The least common multiple of two or more algebraic expressions is the expression of lowest degree which is divisible by each of them without remainder.
LCM OF POLYNOMIALS :
1•Find the LCM of the numerical coefficient of the polynomials.
2•Factorise the given polynomials.
3•Take the highest power of each of the factors (including the ones in common)]
4•The product of the number and the powers of the factors obtained in step 1 and 3 is the LCM of the given polynomials.
Solution:
★ 10 (9x² + 6 x y + y²)
= 2 x 5 (9 x² + 6 x y + y²)
= 2 x 5 ((3 x)² + 2×3x y + (y)²)
= 2 x 5¹ x (3 x + y)²
[a² +2ab + b² = (a+b)²]
★ 12 (3x² - 5 xy - 2y²)
= 2² x 3 (3 x² - 6 x y + x y - 2y²)
[By middle term splitting]
= 2² x 3 x [3 x (x - 2y) + y (x - 2y)]
= 2² x 3¹ x (3 x + y) (x - 2y)
★ 14 (6 x⁴ + 2 x³)
= 2 x 7 x 2 x³ (3 x + 1)
= 2² x 7¹ x x³ (3 x + 1)
L.C.M = 2² x 5¹ x 7¹x 3¹ x x³ x (3 x + y)²(3 x + 1)(x - 2y)
[On taking the highest power of each of the factors (including the ones in common)]
L.C.M= 420 x³ (3 x + y)²(3 x + 1)(x - 2y)
Hence, the L.C.M is 420 x³ (3 x + y)²(3 x + 1)(x - 2y).
- I hope it's help you.