Question

Разложить на множители: 1) (2-3n)²-9n⁴ 2) (а-5)²+2(5-a)+1 3)х⁶-х⁴-х²+1 4)8b³-

Answer 1

$1) (2-3n)^2-9n^4= (2-3n)^2-(3n^2)^2=(2-3n-3n^2)(2-3n+3n^2) \\ \\ 2) (a-5)^2+2(5-a)+1=a^2-10a+25+10-2a+1= \\ \\ a^2-12a+36 =(a-6)^2 \\ \\ 3)x^6-x^4-x^2+1=x^4(x^2-1)-(x^2-1)=(x^4-1)(x^2-1)= \\ \\ (x^2-1)(x^2+1)(x^2-1)=(x^2-1)^2(x^2+1)= \\ \\ (x-1)^2(x+1)^2(x^2+1) \\ \\4) 8b^3- \frac{1}{27}=(2b)^3-( \frac{1}{3})^3=(2b- \frac{1}{3})(4b^2+ \frac{2}{3}b+ \frac{1}{9})$

Answer 2

1) (2-3n)²-9n⁴ = (2-3n)² - (3n)² = (2-3n+3n)(2-3n-3n) = (2-3n+3n)(2-6n) = (2-6n)(2-6n) = (2-6n)²

2) (а-5)²+2(5-a)+1 = (а-5)² - 2(a-5) + 1 = (а-5)(а-5) - 2a + 10 + 1 = (а-5)(а-5) - 2a + 11

3) х⁶-х⁴-х²+1 = (x³)² - (x²)² - x² + 1 = (x³-x²+1)(x³+x²-1)

4) 8b³- = 8b³ - 0 = 8b³