Question

Write the degrees of the following algebraic expressions:

1. 5x²y²z
2. 4x² + 5x²y² + 6
3. ab + ba + ca
4. x + y + z – 3xyz
5. p²q² + a² + pq


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Answer 1

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We know that

(x² + y² + z² + 2xy + 2yz + zx) = (x + y +z)²

(i) 4x² +9y² + 16z² + 12xy - 24yz - 16xz

= (2x)² + (3y)² + (-4z)² + 2(2x)(3y) +

2(3y)(-4z) + 2(-4z)(2x)

= (2x + 3y - 4z)² = (2x + 3y - 4z)(2x + 3y -

4z)

(ii) 2x² + y² + 8z²-2√2xy +4√2yz - 8zx

= (-√2x) + (y)² + (√2z) + 2(-√√2x)(y) +

2(y)(2√/2z) + 2(2√/2z)(y)

= (-√2x + y + 2√/2z)² = (-√√2x+y +

2√2z)(-√2x + y + 2√/2z)

Answer 2

Answer:

. A manufacturing firm is producing x units daily at the total cost of x/20+ 4x + 30.Its demand function is x = 30 - 2p. What should be the production so that marginalrevenue and marginal cost of the firm become