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Expand the brackets in the following expressions. (i) (7x−5)(3x+4)² (ii) (4a−7b)²

Factorise 16h² − 49k²

User Abedfar
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1 Answer

4 votes

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

User SphynxTech
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