Evaluate each of the following algebraic expressions for x = 1, y = -1

1.	Evaluate each of the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:(i) ax + by + cz(ii) ax2 + by2 – cz(iii) axy + byz + cxy
Answer» (i) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2 Consider ax + by + cz On substituting the given values = (-2) (1) + (1) (-1) + (-2) (2) = –2 – 1 – 4 = –7 (ii) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2 Consider ax² + by² – cz On substituting the given values = (-2) × 1² + 1 × (-1)² – (-2) × 2 = 4 + 1 – (-4) = 5 + 4 = 9 (iii) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2 Consider axy + byz + cxy = (-2) × 1 × -1 + 1 × -1 × 2 + (-2) × 1 × (-1) = 2 + (-2) + 2 = 4 – 2 = 2

Evaluate each of the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:(i) ax + by + cz(ii) ax2 + by2 – cz(iii) axy + byz + cxy

Answer»

(i) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2

Consider ax + by + cz

On substituting the given values

= (-2) (1) + (1) (-1) + (-2) (2)

= –2 – 1 – 4

= –7

(ii) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2

Consider ax² + by² – cz

On substituting the given values

= (-2) × 1² + 1 × (-1)² – (-2) × 2

= 4 + 1 – (-4)

= 5 + 4

= 9

(iii) Given x = 1, y = -1, z = 2, a = -2, b = 1, c = -2

Consider axy + byz + cxy

= (-2) × 1 × -1 + 1 × -1 × 2 + (-2) × 1 × (-1)

= 2 + (-2) + 2

= 4 – 2

= 2