Question

16x²-24yz-9y²-16z² factorise the term

Answer 1

16x^2 -24yz-9y^2-16z^2 = (4x)^2 -24yz-(3y)^2-(4z)^2

            = -{(3y)^2+24yz+4z^2} + 4x^2

            = -(3y+4z)^2 + 4x^2    [using a^2+2ab+b^2 = (a+b)^2]

              = (4x)^2 -(3y+4z)^2

              = (4x+3y+4z) (4x-3y-4z)  [using a^2 - b^2 = (a+b)(a-b) where a=4x  &   b=3y+4z]

Answer 2

Answer:

(4x + 3y + 4z)(4x - 3y - 4z)

Step-by-step explanation:

16x² - (24yz - 9y² - 16z²)

= 16x² - (9y² + 24yz + 16z²)

= 16x² - ([3y]² + 2(3y)(4z) + [4z]²)

= 16x² - ([3y + 4z]²)

= (4x)² - (3y + 4z)²

= (4x + 3y + 4z)(4x - (3y + 4z)  ∵ a² - b² = (a + b)(a - b)

= (4x + 3y + 4z)(4x - 3y - 4z)