Exercise 10.2

(i)

(i) x+1

Type: expression

Explanation:
Contains the variable .

(ii)

(ii) 3m2

Type: expression

Explanation:
Contains the variable .

(iii)

(iii) −30+16

Type: expression

Explanation:
Contains only .

(iv)

(iv) 4p2−5q2

Type: expression

Explanation:
Contains the variables and .

(v)

(v) 96

Type: expression

Explanation:
Contains only a .

(vi)

(vi) x2−5yz

Type: expression

Explanation:
Contains the variables , , and .

(vii)

(vii) 215x2yz

Type: expression

Explanation:
Contains the variables , , and .

(viii)

(viii) 95÷5×2

Type: expression

Explanation:
Contains only .

(ix)

(ix) 2+m+n

Type: expression

Explanation:
Contains the variables and .

(x)

(x) 310+15+62

Type: expression

Explanation:
Contains only .

(xi)

(xi) 11a2+6b2−5

Type: expression

Explanation:
Contains the variables and .

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2. State whether the expression is a numerical expression or an algebraic expression

(i)

(i) x+1

x+1 contains This is an expression.

(ii)

(ii) 3m2

3m2 contains This is an expression.

(iii)

(iii) −30+16

−30+16 contains all This is a expression.

(iv)

(iv) 4p2−5q2

4p2−5q2 contains This is an expression.

(v)

(v) 96

96 contains all This is a expression.

(vi)

(vi) x2−5yz

x2−5yz contains This is an expression.

(vii)

(vii) 215x2yz

215x2yz contains This is an expression.

(viii)

(viii) 95÷5×2

95÷5×2 contains all This is a expression.

(ix)

(ix) 2+m+n

2+m+n contains This is an expression.

(x)

(x) 310+15+62

310+15+62 contains all This is a expression.

(xi)

(xi) 11a2+6b2−5

11a2+6b2−5 contains This is an expression.

3. Which of the following multinomials is monomial, binomial or trinomial?

4y−7z

1+x+x2

7mn

a2+b2

100xyz

ax+9

p2−3pq+r

3y2−x2y2+4x

7x2−2xy+9y2−11

Monomial

Binomial

Trinomial

Multimonial

4. What is the degree of each of the monomials?

(i)

(i) 7y

7y has degree

(ii)

(ii) −xy2

−xy2 has degree

(iii)

(iii) xy2z2

xy2z2 has degree

(iv)

(iv) −11y2z2

−11y2z2 has degree

(v)

(v) 3mn

3mn has degree

(vi)

(vi) −5pq2

−5pq2 has degree

5. Find the degree of each algebraic expression.

(i)

(i) 3x−15

3x−15 has degree

(ii)

(ii) xy+yz

xy+yz has degree

(iii)

(iii) 2y2z+9yz−7z−11x2y2

2y2z+9yz−7z−11x2y2 has degree

(iv)

(iv) 2y2z+10yz

2y2z+10yz has degree

(v)

(v) pq+p2q−p2q2

pq+p2q−p2q2 has degree

(vi)

(vi) ax2+bx+c

ax2+bx+c has degree

6. Write any two Algebraic expressions with the same degree.

Here are two pairs of algebraic expressions with the same degree:

Example 1:

(i) x2+y2

x2+y2 has degree

(ii) xy

xy has degree

Both expressions have degree 2 because:

- In x2+y2: highest power is

- In xy: sum of exponents is 1 + 1 =

Example 2:

(i) x2y+xyz

x2y+xyz has degree

(ii) a2b+c3

a2b+c3 has degree

Both expressions have degree 3 because:

- In x2y+xyz: highest sum of exponents is

- In a2b+c3: highest power is

Algebraic Expressions

Glossary

Exercise 10.2

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Example 1:

Example 2:

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Algebraic Expressions

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Glossary

Exercise 10.2

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Example 1:

Example 2: