Question

4a³- 9a and 2a²+3a-9. find HCF and LCM.​

Answer 1

ANSWER:

Given:

• 4a³ - 9a
• 2a² + 3a - 9

To Find:

• HCF and LCM

Solution:

We need to find the HCF and LCM of 4a³ - 9a and 2a² + 3a - 9.

So, we will factorize the expressions.

Factors of 4a³ - 9a:

⇒4a³ - 9a

Taking 'a' common,

⇒a(4a² - 9)

⇒a[(2a)² - (3)²]

As, (a² - b²) = (a + b)(a - b),

So,

⇒a[(2a + 3)(2a - 3)]

⇒a(2a + 3)(2a - 3)

Factors of 2a² + 3a - 9:

⇒2a² + 3a - 9

Splitting the middle term,

⇒2a² + 6a - 3a - 9

Taking common,

⇒2a(a + 3) - 3(a + 3)

⇒(a + 3)(2a - 3)

Now,

Common factors of 4a³ - 9a and 2a² + 3a - 9:

⇒(2a - 3)

So,

⇒HCF = Highest Common Factor

So,

⇒HCF of 4a³ - 9a and 2a² + 3a - 9 = 2a - 3

Now,

All factors of 4a³ - 9a and 2a² + 3a - 9:

⇒a, (2a + 3), (2a - 3), (a + 3)

(We took common factor only once)

So,

⇒LCM = Least Common Multiple

So,

⇒LCM = a(2a + 3)(2a - 3)(a + 3)

⇒LCM = [a(2a + 3)(2a - 3)]×(a + 3)

⇒LCM = (4a³ - 9a)(a + 3)

⇒LCM of 4a³ - 9a and 2a² + 3a - 9 = 4a⁴ + 12a³ - 9a² - 27a