The HCF and LCM of two polynomial p(m, n) and q(m,n) is 4m2(m2 - n2) a

1.	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» 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

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» 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