please i need help on solving this problems, of factorization:
1)3x^6-3x^5-12x^5+12x^4
2)5x^4y^2+20x^3y^2-15x^3y^2-60x^2y^2
3)x^4-x^2y^2
4)x^7y^2-x^4y^2
5)x^5-16x
1)3x^6-3x^5-12x^5+12x^4
2)5x^4y^2+20x^3y^2-15x^3y^2-60x^2y^2
3)x^4-x^2y^2
4)x^7y^2-x^4y^2
5)x^5-16x
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Hello,
3x⁶ - 3x⁵ - 12x⁵ + 12x⁴
= 3x⁴(x² - x - 4x + 4)
= 3x⁴[x(x - 1) - 4(x - 1)]
= 3x⁴(x - 1)(x - 4)
5x⁴y² + 20x³y² - 15x³y² - 60x²y²
= 5x²y²(x² + 4x - 3x - 12)
= 5x²y²[x(x + 4) - 3(x + 4)]
= 5x²y²(x + 4)(x - 3)
x⁴ - x²y²
= x²(x² - y²)
= x²(x - y)(x + y)
x⁷y² - x⁴y²
= x⁴y²(x³ - 1)
= x⁴y²(x - 1)(x² + x + 1)
x⁵ - 16x
= x(x⁴ - 16)
= x(x² + 4)(x² - 4)
= x(x² + 4)(x + 2)(x - 2)
Regards,
Dragon.Jade :-)
3x⁶ - 3x⁵ - 12x⁵ + 12x⁴
= 3x⁴(x² - x - 4x + 4)
= 3x⁴[x(x - 1) - 4(x - 1)]
= 3x⁴(x - 1)(x - 4)
5x⁴y² + 20x³y² - 15x³y² - 60x²y²
= 5x²y²(x² + 4x - 3x - 12)
= 5x²y²[x(x + 4) - 3(x + 4)]
= 5x²y²(x + 4)(x - 3)
x⁴ - x²y²
= x²(x² - y²)
= x²(x - y)(x + y)
x⁷y² - x⁴y²
= x⁴y²(x³ - 1)
= x⁴y²(x - 1)(x² + x + 1)
x⁵ - 16x
= x(x⁴ - 16)
= x(x² + 4)(x² - 4)
= x(x² + 4)(x + 2)(x - 2)
Regards,
Dragon.Jade :-)