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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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)
Answered by
4
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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