Chapter 10: Algebraic Expressions

Solution:-

In the expression 2πr, the algebraic variable is r.

Solution:-

Number of terms in a monomial is 1.

Expression with one term is called a ‘Monomial’.

Solution:-

Like terms in the expression n(n + 1) + 6 (n – 1) are n and 6n.

Consider the given expression, n(n + 1) + 6 (n – 1)

= n² + n + 6n – 6

= n² + 7n – 6

Therefore, like terms are n and 6n

Solution:-

The expression 13 + 90 is a constant.

13 + 90 = 103

Solution:-

The speed of car is 55 km/hrs. The distance covered in y hours is 55y.

Because, distance = speed × time

Solution:-

x + y + z is an expression which is neither monomial nor binomial.

The given expression contains 3 terms so; it is a trinomial.

Solution:-

If (x²y + y² + 3) is subtracted from (3x²y + 2y² + 5), then coefficient of y in the result is 2x².

(x²y + y² + 3) is subtracted from (3x²y + 2y² + 5)

= (3x²y + 2y² + 5) – (x²y + y² + 3)

= 3x²y + 2y² + 5 – x²y – y² – 3

= (3x²y – x²y) + (2y² – y²) + (5 – 3)

= 2x²y + y² + 2

Solution:-

– a – b – c is same as – a – (b + c).

Solution:-

The unlike terms in perimeters of following figures are 2y and 2y².

We know that, perimeter of rectangle = 2 (length + breadth)

= 2 (2x + y)

= 4x + 2y

The unlike terms in perimeters of following figures are 2y and 2y².

Perimeter of parallelogram = x + x + y² + y²

= 2x + 2y²

Solution:-

On adding a monomial 2x or -4y² or -z to – 2x + 4y² + z, the resulting expression becomes a binomial.

2x + (-2x + 4y² + z) = 2x – 2x + 4y² + z

= 4y² + z

-4y² + (-2x + 4y² + z) = -4y² – 2x + 4y² + z

= – 2x + z

-z + (-2x + 4y² + z) = -z – 2x + 4y² + z

= -2x + 4y²