Question

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

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)

Answer 2

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)