Factorise the following:
Answers
Answer:
a) 4x² - 36y²
= (2x)² - (6y)²
using a² − b² = (a + b)(a − b)
= (2x + 6y)(2x - 6y)
∴ 4x² - 36y² = (2x + 6y)(2x - 6y)
b) 4x³ - 32y³
= 4 × (x³ - 8y³)
= 4 × [x³ - (2y)³]
using a³ − b³ = (a − b)(a² + ab + b² )
= 4 × (x - 2y)× (x² + 2xy + 4y²)
∴ 4x³ - 32y³ = 4 × (x - 2y)× (x² + 2xy + 4y²)
c) 40x³ - 320y³
= 40 × (x³ - 8y³)
= 40 × [x³ - (2y)³]
using a³ − b³ = (a − b)(a² + ab + b² )
= 40 × (x - 2y)× (x² + 2xy + 4y²)
∴ 40x³ - 320y³ = 40 × (x - 2y)× (x² + 2xy + 4y²)
d) 64x⁴ - 625
= (4x²)² - 25²
using a² − b² = (a + b)(a − b)
= (4x² + 25) (4x² - 25)
∴ 64x⁴ - 625 = (4x² + 25) (4x² - 25)
f) 2x² + 3√5x + 5 and h) 2x² - x + 1/8
It has no root
g) (a + b)³ - 8
= (a + b)³ - 2³
using a³ − b³ = (a − b)(a² + ab + b² )
= (a + b - 2)[(a + b)² + (a+b)(2) + 4]
= (a + b - 2)[(a² + 2ab + b²) + 2a + 2b + 4]
= (a + b - 2)(a² + 2ab + b² + 2a + 2b + 4)
∴ (a + b)³ - 8 = (a + b - 2)(a² + 2ab + b² + 2a + 2b + 4)
i) 3(a + 5)² - 2(a + 5) - 8
put (a + 5) = x
= 3x² - 2x - 8
= 3x² - 12x + 2x - 8
= 3x(x - 4) - 2(x - 4)
= (3x - 2)(x - 4)
resubstitude x = a + 5
= [3(a + 5) - 2] [(a + 5) - 4]
= (3a + 15 - 2)(a + 5 - 4)
= (3a + 13)(a + 1)
∴ 3(a + 5)² - 2(a + 5) - 8 = (3a + 13)(a + 1)
Step-by-step explanation:
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