Question

x = (a+b)2, y = a2+2ab+b2 and z = a2+b2-2ab (a) determine the sum of the numerical co-efficients of z terms. (b) determine y+z and y-z (c) If a = 3 and b = - 2, Prove that x = y​

Answer 1

The given equations are;

x = (a + b)²

y = a² + 2·a·b + b²

z = a² + b² - 2·a·b

(a) The numerical coefficients of z terms are

1, 1, -2

The sum of the numerical coefficients = 1 + 1 - 2 = 0

(b) y + z is found by substituting the values of 'y' and 'z', in the expression y + z, as follows;

y + z = a² + 2·a·b + b² + a² + b² - 2·a·b = 2·a² + 2·b²

y + z = 2·a² + 2·b²

y - z = a² + 2·a·b + b² - (a² + b² - 2·a·b) = 4·a·b

(c) Given that a = 3, and b = -2, we have;

x = (a + b)² = a² + a·b + a·b + b² = a² + 2·a·b + b² = y

Therefore, x = y, for all values of 'a', and 'b'

Explanation: