Question

Выделите полный квадрат из многочлена   а)4+2q+q^2    б)x^2+6x+1                                                в)a^2-4a+1      г)m^2-6m+9        д)16+8p+p^2     е)a^2-2a

Answer 1

a)  4+2q+q^2= (2+q)^2

б)  x^2+6x+1=x^2+6x+1+8-8 = x^2+6x+9 - 8 = (x+3)^2 - 8

в)  a^2-4a+1= a^2-4a+1 +3 - 3=a^2-4a+4 -3 = (a-2)^2-3

г)  m^2-6m+9=(m-3)^2

д) 16+8p+p^2 = (4+p)^2

е) a^2-2a= a^2-2a +1 -1= (a-1)^2 -1

Answer 2

а)4+2q+q^2: We can try to complete the square by adding and subtracting a constant value that would turn the quadratic expression into a perfect square. To do this, we need to take half of the coefficient of the q-term, square it, and add that value both inside and outside the parentheses:

4 + 2q + q^2 = (q + 1)^2 - 1

So, the full square is (q + 1)^2.

б)x^2+6x+1: We can complete the square by adding and subtracting a constant value that would turn the quadratic expression into a perfect square. To do this, we need to take half of the coefficient of the x-term, square it, and add that value both inside and outside the parentheses:

x^2 + 6x + 1 = (x + 3)^2 - 8

So, the full square is (x + 3)^2.

в)a^2-4a+1: We can complete the square by adding and subtracting a constant value that would turn the quadratic expression into a perfect square. To do this, we need to take half of the coefficient of the a-term, square it, and add that value both inside and outside the parentheses:

a^2 - 4a + 1 = (a - 2)^2 - 3

So, the full square is (a - 2)^2.

г)m^2-6m+9: We can complete the square by adding and subtracting a constant value that would turn the quadratic expression into a perfect square. To do this, we need to take half of the coefficient of the m-term, square it, and add that value both inside and outside the parentheses:

m^2 - 6m + 9 = (m - 3)^2

So, the full square is (m - 3)^2.

д)16+8p+p^2: We can try to complete the square by adding and subtracting a constant value that would turn the quadratic expression into a perfect square. To do this, we need to take half of the coefficient of the p-term, square it, and add that value both inside and outside the parentheses:

16 + 8p + p^2 = (p + 4)^2 - 16

So, the full square is (p + 4)^2.

е)a^2-2a: We can complete the square by adding and subtracting a constant value that would turn the quadratic expression into a perfect square. To do this, we need to take half of the coefficient of the a-term, square it, and add that value both inside and outside the parentheses:

a^2 - 2a = (a - 1)^2 - 1

So, the full square is (a - 1)^2.