Question

N 28.4: Преобразуйте квадрат двучлена в многочлен стандартного вида:а)(-x+1)² б)(-z -3)²в)(-n+8)²г)(-m-10)²

Answer 1

А) х2-2х+1
б) z2+6z+9
в) n2-16n+64
г) m2+20m+100

Answer 2

Converting Squares of Binomials to Standard Form Polynomials

a) (-x + 1)²

To convert the square of the binomial (-x + 1) to a standard form polynomial, we can use the formula for squaring a binomial: (a - b)² = a² - 2ab + b².

So, for (-x + 1)²: (-x + 1)² = (-x)² - 2(-x)(1) + 1² = x² - 2x + 1

Therefore, the standard form of the polynomial (-x + 1)² is x² - 2x + 1[[1]].

b) (-z - 3)²

Similarly, for (-z - 3)²: (-z - 3)² = (-z)² - 2(-z)(3) + 3² = z² + 6z + 9

Hence, the standard form of the polynomial (-z - 3)² is z² + 6z + 9[[2]].

c) (-n + 8)²

For (-n + 8)²: (-n + 8)² = (-n)² - 2(-n)(8) + 8² = n² - 16n + 64

So, the standard form of the polynomial (-n + 8)² is n² - 16n + 64[[3]].

d) (-m - 10)²

Finally, for (-m - 10)²: (-m - 10)² = (-m)² - 2(-m)(10) + 10² = m² + 20m + 100

Therefore, the standard form of the polynomial (-m - 10)² is m² + 20m + 100[[4]].