​ Simplify each of the following products: (i) (1/2a - 3b)(3b + 1/2a)(1/4a^2 + 9b^2) (ii) (m + n/7)^3(m - n/7)

Question

Simplify each of the following products:

(i) \((\frac{1}{2}a-3b)(3b+\frac{1}{2}a)(\frac{1}{4}a^2+9b^2)\)

(ii) \((m+\frac{n}{7})^3(m-\frac{n}{7})\)

(iii) \((\frac{x}{2}-\frac{2}{5})(\frac{2}{5}-\frac{x}{2})\) - x² + 2x

(iv) (x² + x – 2) (x² - x + 2)

(v) (x³ - 3x² – x) (x² - 3x + 1)

(vi) (2x⁴ - 4x² + 1) (2x⁴ - 4x² - 1)

Answer 1

(i) On rearranging we get, \((\frac{1}{2}a-3b)(3b+\frac{1}{2}a)(\frac{1}{4}a^2+9b^2)\)

(ii) On rearranging we get, \((m+\frac{n}{7})^3(m-\frac{n}{7})\)

(iii) On rearranging we get,   \((\frac{x}{2}-\frac{2}{5})(\frac{2}{5}-\frac{x}{2})\) - x² + 2x

(iv) Using the idendity, (a+b)(a - b) = a² - b²

On rearranging we get,

(v) Taking x as common factor, we write, 

(vi) On Reaaranging we get,