Question

The HCF and LCM of two polynomial p(m, n) and q(m,n) is 4m²(m² - n²) and (m³ – n³) respectively then what is the value of p(m, n) × q(m, n)?
1. 4m⁷ + 4m²n⁵ – 4m⁴n² (m + n)
2. 4m⁷ + 4m²n⁵ –m⁴n² (4m + n)
3. m⁵ + m²n⁵ –m⁴n² (m + n)
4. 2m⁵ + m²n⁵ – 8m⁴n² (m + n)

Answer 1

Correct Answer - Option 1 : 4m⁷ + 4m²n⁵ – 4m⁴n² (m + n)

Given:

The HCF and LCM of polynomial p(m, n) and q(m, n) is 4m²(m² - n²) and (m³ – n³)

Formula used:

Product of polynomial = Product of HCF and LCM of polynomials

p(x) × q(x) = LCM of (p(x) and q(x)) × HCF of (p(x) and q(x))

Calculation:

By using the given formula Product of polynomial = Product of HCF and LCM of polynomials

∴ p(m, n) × q(m, n) = LCM of (p(m, n) and q(m, n)) × HCF of (p(m, n) and q(m, n))

⇒ p(m, n) × q(m, n) = 4m²(m² - n²) × (m³ – n³)

⇒ p(m, n) × q(m, n) = 4m² {m⁵ + n⁵ – m²n² (m + n)}

⇒ p(m, n) × q(m, n) = 4m⁷ + 4m²n⁵ – 4m⁴n² (m + n)

Hence, option (1) is correct