### Exercise-12.1

Question 1:

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 numbers m and n.

(vii) Product of number y and z subtracted from 10.

(viii) Sum of numbers a and b subtracted from their product.

Answer:

(i) y – x

(ii)1/2( x+y )

(iii)Z^{2}

(iv) 1/4( pq )

(v)x^{2}+y^{2}

(vi)5 + 3 (mn)

(vii) 10 -(yz)

(viii) ab-(a+b)

Question 2:

(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.

(a) x – 3

(b) 1 + x + x^{2}

(c) y – y^{3}

(d) 5xy^{2} + 7x^{2}y

(e) -ab + 2b^{2} – 3a^{2}

(ii) Identify terms and factors in the expression given below:

(a) -4x + 5

(b) -4x + 5y

(c) 5y + 3y^{2}

(d) xy + 2x^{2}y^{2}

(e) pq + q

### Exercise-12.2

Question 1:

**Simplify combining like terms:**

(i) 21b – 32 + 7b – 20b

(ii)-z^{2} + 13z^{2} – 5z + 7z^{3} -15z

(iii) p -(p – q) – q – (q – p)

(iv) 3a – 2b – ab -(a – b + ab) + 3ab + b -a

(v) 5x^{2}y -5x^{2} + 3yx^{2} -3y^{2} + x^{2 }– y^{2} + 8xy^{2} -3y^{2}

(vi) (3y^{2} + 5y -4) – (8y – y^{2} -4)

Answer:

The parts of the given questions are solved as follows:

(i) It is given in the question that,

We have to simplify the expression by combining like terms:

21b – 32 + 7b – 20b

= 21b – 20d +7b – 32

= (21 – 20 + 7)b – 32

= 8b – 32

(ii) It is given in the question that,

We have to simplify the expression by combining like terms:

-z^{2} + 13z^{2} – 5z + 7z^{3} -15z

= – z2 + 13z2 + 7z3 – 5z – 15z

= z2(- 1 + 13) + 7z3 – z(5+15)

= 12z2 + 7z3 – 20z

(iii) It is given in the question that,

We have to simplify the expression by combining like terms:

p -(p – q) – q – (q – p)

= p – p + q – q – q +p

= p – p + p + q – q – q

= p – q

(iv) It is given in the question that,

We have to simplify the expression by combining like terms:

3a – 2b – ab -(a – b + ab) + 3ab + b -a

= 3a – 2b – ab – a + b – ab + 3ab + b – a

= 3a – a – a – 2b + b + b – ab – ab + 3ab

= (3 – 1 – 1)a–b(2 – 1 – 1) -ab(1 + 1 – 3)

= a + ab

(v) It is given in the question that,

We have to simplify the expression by combining like terms:

5x^{2}y -5x^{2} + 3yx^{2} -3y^{2} + x^{2 }– y^{2} + 8xy^{2} -3y^{2}

= 5x2y + 3x2y – 5×2 + x2 – 3y2 –y2 – 3y2 + 8xy2

= (5 + 3)x2y + (– 5 + 1)x2 + (– 3 – 1 – 1)y2 + 8xy2

= 8x2y – 4×2 – 5y2 + 8xy2

(vi) It is given in the question that,

We have to simplify the expression by combining like terms:

(3y^{2} + 5y -4) – (8y – y^{2} -4)

= 3y2+ 5y – 4 – 8y + y2 + 4

= 3y2 + y2 + 5y – 8y – 4 + 4

= 4y2 – 3y