Question

Q.
Factorise each of the following expressions completely.

I: -25π⁴y² – 15πx³
II: 5a(3c + 5d) + 10b(3c + 5d)
III: a²b² – 5a²b-5ab² + ab³
IV: x³ – x² - 1 + x
V: (x + 3y)² – (x + 3y)(3x – 7y)
VI: 5a(4p - q) - 10b(q - 4p)​

Answer 1

Step by step explanation:

$({i})\: - 25 {\pi}^{4} {y}^{2} - 15\pi {x}^{3} \\ - 5\pi (5 {\pi}^{3} {y}^{2} + 3 {x}^{3} ) \\ (ii) \: (5a + 10b)(3c + 5d) \\ (iii) \: {a}^{2} b(b - 5) + a {b}^{2} ( - 5 + b) \\ {a}^{2} b(b - 5) + a {b}^{2} (b - 5) \\( {a}^{2} b + a {b}^{2} )(b - 5) \\ (iv)x^2(x-1)+1(-1+x)\\ {x}^{2}(x-1)+1(x-1)//({x}^{2}+1)(x-1)\\(v){x}^{2}+3xy+9{y}^{2} -x (3x-7y)-3y(3x-7y)\\3{x}^{2}+7xy-9xy+21{y}^{2}\\x(3x+7y)+3y(3x+7y)\\(x+3y)(3x+7y)\\(vi)5a(4p-q)+10b(4p-q)\\(5a+10b)(4p-q)$

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