Question

4. factorise. ¡) a²-b^4. ¡¡) p^4-81. ¡¡¡) x^4-(y+z)^4. ¡v) x^4-(x-z) ^4. v) a^4-2a²b²+b^4​

Answer 1

Step-by-step explanation:

i) a² - b⁴

= a² - (b²)²

= (a + b²) (a - b²)

ii) p⁴ - 81

= (p²)² - 9²

= (p² + 9) (p² - 9)

= (p² + 9) (p² - 3²)

= (p² + 9) (p + 3) (p - 3)

iii) x⁴ - (y + z)⁴

= (x²)² - {(y + z)²}²

= {x² + (y + z)²} {x² - (y + z)²}

= {x² + (y² + z² + 2yz)} [{x + (y + z)} {x - (y + z)}]

= (x² + y² + z² + 2yz) (x + y + z) (x - y - z)

iv) x⁴ - (x - z)⁴

= (x²)² - {(x - z)²}²

= {x² + (x - z)²} {x² - (x - z)²}

= {x² + (x² + z² - 2xz)} [{x + (x - z)} {x - (x - z)}]

= (x² + x² + z² - 2xz) (x + x - z) (x - x + z)

= (2x² + z² - 2xz) (2x - z) (z)

= z (2x² + z² - 2xz) (2x - z)

v) a⁴ - 2a²b² + b⁴

= (a² - b²)²

= {(a + b) (a - b)}²

= (a + b)² (a - b)²

= (a² + b² + 2ab) (a² + b² - 2ab)

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