factorise the following expressions:- (i) a³ – 27 (ii) 1 – 27x³ (iii) 8x³ – (2x – 3y)³ (IV) a⁸ – a²b⁶ (v) a³- 5 underroot5 b³

August 16, 2021

By Camila

2 thoughts on “factorise the following expressions:- (i) a³ – 27 (ii) 1 – 27x³ (iii) 8x³ – (2x – 3y)³ (IV) a⁸ – a²b⁶ (v) a³- 5 underroot5 b³<br /”

1. Answer:

   (i)a³-27

   = a³-3³

   = (a-3)(a²+3a+9)

   (ii) 1-27x³

   = 1³-(3x)³

   = (1-3x)(1+3x+9x²)

   (iii) 8x³–(2x-3y)³

   = (2x)³-(2x-3y)³

   = (2x-(2x-3y)){(2x)²+2x(2x-3y)+(3y)²}

   = (2x-2x+3y)(4x²+4x²-6xy+9y²)

   = 3y(8x²-6xy+9y²)

   (iv)a⁸-a²b⁶

   = a²(a⁴-b⁶)

   = a²{(a²)²-(b³)²}

   = a²(a²-b³)(a²+b³)

   (v)a³-5√5b³

   = a³-(√5b)³

   = (a-√5b)(a²+√5ab+5b²)

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2. Answer:

   1. (−3)(²+3+9)

   2.The expression is not factorable with rational numbers.

   3.y(y²−6x(y−2x))

   4. 2a²b³

   5. (a-√2b) (a²+2b² + √2ab)

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