Chapter 10: Algebraic Expressions

Solution:-

True.

When we subtract a monomial from a trinomial, then answer can be binomial or polynomial.

For example: subtract p² from p² + q² – r²

= (p² + q² – r²) – p²

= p² + q² – r² – p²

= q² – r²

Solution:-

False.

When we add a monomial and a trinomial, then answer can be binomial or trinomial.

For example: add p² and p² + q² – r²

= p² + (p² + q² – r²)

= p² + p² + q² – r²

= 2p² + q² – r²

Solution:-

From the question it is given that,

x is multiplied by itself = x × x = x²

the product of x and y = x × y = xy

Then, As per the condition in the question = x² + xy

Therefore, the obtained expression is binomial.

(b) Three times of p and two times of q are multiplied and then subtracted from r.

Solution:-

From the question it is given that,

Three times of p = 3p

Two times of q = 2q

Three times of p and two times of q are multiplied = 3p × 2q =3p2q

Then, As per the condition in the question = r – 3p2q

Therefore, the obtained expression is binomial.

(c) Product of p, twice of q and thrice of r.

Solution:-

As per the condition given in the question,

p × 2q × 3r = 6pqr

Therefore, the obtained expression is a monomial.

(d) Sum of the products of a and b, b and c and c and a.

Solution:-

The products of a and b, b and c and c and a = (a × b) and (b × c) and (c × a)

Then, sum of the products of a and b, b and c and c and a = ab + bc + ca

Therefore, the obtained expression is trinomial.

(e) Perimeter of an equilateral triangle of side x.

Solution:-

We know that, perimeter of triangle = sum of all sides

= x + x + x

= 3x

Therefore, the obtained expression is monomial.

(f) Perimeter of a rectangle with length p and breadth q.

Solution:-

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

= 2 (p + q)

= 2p + 2q

Therefore, the obtained expression is binomial.

(g) Area of a triangle with base m and height n.

Solution:-

We know that, area of triangle = ½ × base × height

= ½ × m × n

= ½mn

Therefore, the obtained expression is monomial.

(h) Area of a square with side x.

Solution:-

We know that, area of square = side × side

= x × x

= x²

Therefore, the obtained expression is monomial.

(i) Cube of s subtracted from cube of t.

Solution:-

As per the condition given in the question, t³ – s³

Therefore, the obtained expression is binomial.

(j) Quotient of x and 15 multiplied by x.

Solution:-

Quotient of x and 15 = x ÷ 15

As per the condition given in the question, Quotient of x and 15 multiplied by

x = (x ÷ 15)x

= x²/15

Therefore, the obtained expression is monomial.

(k) The sum of square of x and cube of z.

Solution:-

As per the condition given in the question = x² + z³

Therefore, the obtained expression is binomial.

(l) Two times q subtracted from cube of q.

Solution:-

As per the condition given in the question = q³ – 2q

Therefore, the obtained expression is binomial.

Solution:-

The coefficient of x² in the given expression is 1.

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

(ii) x³ – 2x² + 3x + 1

Solution:-

The coefficient of x² in the given expression is -2.

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

(iii) 1 + 2x + 3x² + 4x³

Solution:-

The coefficient of x² in the given expression is 3.

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

(iv) y + y²x + y³x² + y⁴x³

Solution:-

The coefficient of x² in the given expression is y³.

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

Solution:-

Numerical coefficient of,

x³y²z = 1

xy²z³ = 1

–3xy²z³ = -3

5x³y²z = 5

–7x²y²z² = -7

(ii) 10xyz, –7xy²z, –9xyz, 2xy²z, 2x²y²z

Solution:-

Numerical coefficient of,

10xyz = 10

–7xy²z = -7

–9xyz = -9

2xy²z = 2

2x²y²z = 2