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Question -

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
(i) Subtraction of z from y.
(ii) One half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and 2 subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.



Answer -

(i) Subtraction of z from y
Expression: y – z

(ii)One half of the sum of numbers x and y
Expression: 
1/2(x+y) or (x+y)/2

(iii) The number 2 multiplied by itself.
Expression: z × z = z2

(iv)One-fourth of the product of numbers p and q
Expression: (1/4)pq or pq/4

(v) Numbers x and y both squared and added
Expression: x2 + y2

(vi) Number 5 added to three times the product of number m and n
Expression: 3mn + 5

(vii) Product of numbers y and z subtracted from 10
Expression: 10 – yz

(viii) Sum of numbers a and 6 subtracted from their product
Expression: Sum = a + b, Product = ab
Required expression
= ab – (a + b)
= ab – a- b

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