**1. Classify the algebraic expressions as monomials, binomials and trinomials.**

a. 6x^{2} + 3

b. 5x^{4}

c. 2a^{2} + 6a +3

d. xy + 3y^{2}

e. x^{3}y^{4}z^{3}

**Ans:**

a. Binomial

b. Monomial

c. Trinomial

d. Binomial

e. Monomial

**Must Read: Up-Hill Stanza-Wise Summary**

**2. Add the following algebraic expressions.**

a. 3x, 5x, (-9x) and 2x

b. xy^{2} + 3x + 5, 4xy^{2} + (-8x)

c. 9x^{2} – xy + 8y^{2}, (-4x^{2}) + 3xy – 2y^{2} and 5x^{2} + 2xy +7y^{2}

**Ans:**

a. = 3x + 5x + (-9x) + 2x

= 10x + (-9x)

= 10x – 9x

= x

b. = [xy^{2} + 3x + 5] + [4xy^{2} + (-8x)]

= [xy^{2} + 3x + 5] + [4xy^{2} – 8x]

= xy^{2} + 3x +5 + 4xy^{2} – 8x

= xy^{2} + 4xy^{2} + 3x – 8x + 5

= 5xy^{2} – 5x + 5

c. = [9x^{2} – xy + 8y^{2}] + [(-4x^{2}) + 3xy – 2y^{2}] + [5x^{2} + 2xy +7y^{2}]

= [9x^{2} – xy + 8y^{2}] + [-4x^{2} +
3xy – 2y^{2}] + [5x^{2} + 2xy +7y^{2}]

= 9x^{2} – xy + 8y^{2} – 4x^{2} + 3xy
– 2y^{2} + 5x^{2} + 2xy + 7y^{2}

= 9x^{2} – 4x^{2 }+ 5x^{2} – xy + 3xy
+ 2xy + 8y^{2} – 2y^{2} + 7y^{2}

= 10x^{2} + 4xy + 13y^{2}

**3. Subtract the following expressions.**

a. 6pqr from 8pqr

b. 2a^{2}bc + 6ab – 5 from -4a^{2}bc + 5ab + 6

c. 6a^{4} – 9a^{3} – 4a from 7a^{4} + 6a^{3} – 13a

**Ans:**

a. = 8pqr – 6pqr

= 2pqr

b. = (-4a^{2}bc + 5ab + 6) – (2a^{2}bc + 6ab – 5)

= -4a^{2}bc + 5ab
+ 6 – 2a^{2}bc – 6ab + 5

= -4a^{2}bc – 2a^{2}bc
+ 5ab – 6ab + 6 + 5

= -6a^{2}bc – ab +
11

c. = (7a^{4} + 6a^{3} – 13a) – (6a^{4} – 9a^{3} – 4a)

= 7a^{4} + 6a^{3}
– 13a – 6a^{4} + 9a^{3} + 4a

= 7a^{4} – 6a^{4}
+ 6a^{3} + 9a^{3} – 13a + 4a

= a^{4} + 15a^{3}
– 9a

**4. Subtract the sum of 2.5a ^{2}b + 5ab + 4 and 5.1a^{2}b + 7ab – 8 from 6.5a^{2}b + 7ab – 10**

**Ans: = **6.5a^{2}b + 7ab – 10 – (2.5a^{2}b
+ 5ab + 4 + 5.1a^{2}b + 7ab – 8)

= 6.5a^{2}b + 7ab – 10 – (2.5a^{2}b + 5.1a^{2}b
+ 5ab + 7ab + 4 – 8)

= 6.5a^{2}b + 7ab – 10 – (7.6a^{2}b + 12ab – 4)

= 6.5a^{2}b + 7ab – 10 – 7.6a^{2}b – 12ab + 4

= 6.5a^{2}b – 7.6a^{2}b + 7ab – 12ab – 10 + 4

= -1.1a^{2}b – 5ab – 6

**5. Two adjacent sides of a rectangle are 3a ^{2} – 6b^{2} and 2a^{2} + 8b^{2}. What will be the perimeter?**

**Ans: **Length of the rectangle: 3a^{2}
– 6b^{2}

Breadth of the rectangle: 2a^{2} + 8b^{2}

Perimeter of rectangle: 2(l+b)

Therefore,

= 2(3a^{2} – 6b^{2} + 2a^{2} + 8b^{2})

= 2(3a^{2} + 2a^{2} – 6b^{2} + 8b^{2})

= 2(5a^{2} + 2b^{2})

= 10a^{2} + 4b^{2}

**6. What should be added to 6a ^{2} – 3b^{2} to get 4a^{2} – 5ab + 4b^{2}?**

**Ans:** To get the number we will need to
subtract **6a ^{2} – 3b^{2 }**from

**4a**Therefore,

^{2}– 5ab + 4b^{2}.= 4a^{2} – 5ab + 4b^{2} – (6a^{2} –
3b^{2})

= 4a^{2} – 5ab + 4b^{2} – 6a^{2} + 3b^{2}

= 4a^{2} – 6a^{2} – 5ab + 4b^{2} + 3b^{2}

= -2a^{2} – 5ab + 7b^{2}

**7. What should be subtracted from 19a ^{3} + 6a^{2}b^{2} to get 4a^{3} – 4a^{2}b^{2} + 6?**

**Ans: **To get the number, we will subtract **4a ^{3} – 4a^{2}b^{2}
+ 6** from

**19a**. Therefore,

^{3}+ 6a^{2}b^{2}= 19a^{3} + 6a^{2}b^{2} – (4a^{3}
– 4a^{2}b^{2} + 6)

= 19a^{3} + 6a^{2}b^{2} – 4a^{3}
+ 4a^{2}b^{2} – 6

= 19a^{3} – 4a^{3} + 6a^{2}b^{2}
+ 4a^{2}b^{2} – 6

= 15a^{3} + 10a^{2}b^{2} – 6

So, this was Exercise 1 of Algebraic Expressions. Stay tuned for more exercises.