Question

Розкладіть на множники: a) m^2 + 2mn + n^2 - k^2 б) 9/16 а^2 - 4х^2 - 4ху - у^2 в) а^2 - 8а - б^2 + 16

Answer 1

Відповідь:

1. Розкладіть на множники:

a) m^2 + 2mn + n^2 - k^2= (m+n-k) * (m+n+k)

б) 9/16 а^2 - 4х^2 - 4ху - у^2= 19\16a²-(2x+y)²= (3\4a-(2x+y)) * (3\4a+(2x+y))= (3\4a-2x-y) * (3\4a+2x+y)

в) а^2 - 8а - б^2 + 16= (a-4)²- 6²= (a-4-6) * (a-4+6)= (a-10) * (a+2)

Пояснення:

Answer 2

a) m^2 + 2mn + n^2 - k^2

This expression cannot be factored further because it does not follow any specific factorization pattern.

b) 9/16 a^2 - 4x^2 - 4xy - y^2

This expression can be factored as follows: (3/4a - 2x - y)(3/4a + 2x + y)

c) a^2 - 8a - b^2 + 16

This expression can be factored as: (a - 4)^2 - b^2 [(a - 4) - b][(a - 4) + b]