Answer:
see explanation
Explanation:
(i)
(7x - 5)(3x + 4)² ← expand (3x + 4)² using FOIL
= (7x - 5)(9x² + 12x + 12x + 16)
= (7x - 5)(9x² + 24x + 16)
each term in the second factor is multiplied by each term in the first factor, that is
7x(9x² + 24x + 16) - 5(9x² + 24x + 16) ← distribute parenthesis
= 63x³ + 168x² + 112x - 45x² - 120x - 80 ← collect like terms
= 63x³ + 123x² - 8x - 80
(ii)
(4a - 7b)²
= (4a - 7b)(4a - 7b) ← expand using FOIL
= 16a² - 28ab - 28ab + 49b² ← collect like terms
= 16a² - 56ab + 49b²
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16h² - 49k² ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
then
16h² - 49k²
= (4h)² - (7k)²
= (4h - 7k)(4h + 7k) ← in factored form