Question

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 − cz²
(iii) axy + byz + cxy

Answer 1

We have x = 1, y = −1, z = 2, a = −2, b = 1 and c = −2.
Thus,
(i) ax + by + cz
= (-2)(1) + (1)(-1) + (-2)(2)
= - 2 + (- 1) + (- 4)
= - 2 -1 - 4 = -7

(ii) ax² + by² - cz²
= (-2)(1)² + (1)(-1)² - (-2)(2)²
= -2 x 1 + 1 - (-2 x 4)
= -2 + 1 - (-8)
= -2 + 1 + 8
= -2 + 9
= 7

(iii) axy + byz + cxy
= (-2)(1)(-1) + (1)(-1)(2) + (-2)(1)(-1)
= 2 + (-2) + 2
= 2 - 2 + 2
= 4 - 2
= 2