AP State Syllabus AP Board 7th Class Maths Solutions Chapter 10 Algebraic Expressions InText Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 10th Lesson Algebraic Expressions InText Questions

Question 1.

In the expressions given below identify all the terms. (Page No. 194)

i) 5x^{2} + 3y + 7

ii) 5x^{2}y + 3

iii) 3x^{2}y

iv) 5x – 7

v) 5x + 8 – 2(-y)

vi) 7x^{2} – 2x

Solution:

i) 5x^{2} + 3y + 7 is a trinomial

ii) 5x^{2}y + 3 is a binomial

iii) 3x^{2}y is a monomial

iv) 5x – 7 is a binomial

v) 5x + 8 – 2 (-y) is a trinomial

vi) 7x^{2} – 2x is a binomial

Question 2.

Write the following expressions in statements. (Page No. 195)

12x, 12, 25x, -25, 25y, 1, x, 12y, y, 25xy, 5x^{2}y, 7xy^{2}, 2xy, 3xy^{2}, 4x^{2}y.

Solution:

Like terms Groups → {12x, 25x, x}

→ {-25, 12, 1}

→ {25y, 12y, 1}

→ {25xy, 2xy}

→ {5x^{2}y,4x^{2}y}

→ {7xy^{2}, 3xy^{2}}

Try This

Question 1.

i) What is the numerical coefficient of ‘x’ ? (Page No. 195)

Solution:

The numerical coefficient of ‘x’ is 1.

ii) What is the numerical coefficient of -‘y’ ?

Solution:

The numerical coefficient of -y is -1.

iii) What is the literal coefficient of ‘-3z’ ?

Solution:

z.

iv) Is a numerical coefficient a constant ?

Solution:

Yes.

v) Is a literal coefficient always a variable ?

Solution:

Yes.

Question 2.

Write 3 algebraic expressions with 3 terms each. (Page No. 196)

Solution:

i) ax^{2} + bx + c

ii) px + qy + rz

iii) x^{2} + y^{2} + z^{2}

Do This

Question 1.

State true or false and give reasons for your answer. (Page No. 195)

i) 7x^{2} and 2x are unlike terms.

ii) pq^{2} and – 4pq^{2} are like terms.

iii) xy, – 12x^{2}y and 5xy^{2} are like terms.

Solution:

i) 7x^{2} and 2x are unlike terms is true. Since the power of the variable x is not same in both the terms.

ii) pq^{2} and – 4pq^{2} are like terms is true. Since both the terms are having same variables and same exponents.

iii) xy, -12x^{2}y and 5xy^{2} are like terms is false. Since all the terms are not contains same exponents.

Question 2.

How many terms are there in each of the following expressions ?

i) x + y

ii) 11x – 3y – 5,

iii) 6 x^{2} + 5x – 4

iv) x^{2}z + 3

v) 5x^{2}y

vi) x + 3 + y

vii) x – \(\frac{11}{3}\)

viii) \(\frac{3 x}{7 y}\)

ix) 2z – y

x) 3x + 5 (Page No. 196)

Solution:

One term – (v) 5x^{2}y, viii) \(\frac{3 x}{7 y}\)

Two terms – (i) x + y , (iv) x^{2}z + 3, (vii) x – \(\frac{11}{3}\), (ix) 2z – y (x) 3x + 5

Three terms – (ii) 11x – 3y – 5, (iii) 6x^{2} + 5x – 4, (vi) x + 3 + y

Question 3.

Give two examples for each type of algebraic expression. ( Page No. 197)

Solution:

Monomial : i) 5x^{2}y, ii) \(\frac{3}{2}\) xyz

Binomial :i) ax + by, ii) 2z – 5

Trinomial : i) ax + by + cz, ii) p^{2} + q^{2} + r^{2
}Polynomial: i) 5x^{4} – 2x^{2} + x – 1, ii) 6 + 5x – 4x^{2} + 3y^{3} – 2z^{4}

Question 4.

Identify the expressions given below as monomial, binomial, trinomial, and multinomial. (Page No. 197)

i) 5x^{2} + y + 6

ii) 3xy

iii) 5x^{2}y + 6x

iv) a + 4x – xy + xyz

Solution:

i) 5x^{2} + y + 6 → is a trinomial.

ii) 3xy → is a monomial.

iii) 5x^{2}y + 6x → is a binomial.

iv) a + 4x – xy + xyz → is a multinomial.

Question 5.

Find the sum of the like terms. (Page No. 200)

i) 5x, 7x

ii) 7x^{2}y, -6x^{2}y

iii) 2m, 11m

iv) 18ab, 5ab, 12ab

v) 3x^{2}, -7x^{2}, 8x^{2
}vi) 4m^{2}, 3m^{2}, -6m^{2}, m^{2
}Solution:

i) 5x + 7x = 12x

ii) 7x^{2}y + (-6x^{2}y) = (7 – 6) x^{2}y = x^{2}y

iii) 2m + 11m = (2 + 11)m = 13m

iv) 18ab + 5ab + 12ab = (18 + 5 + 12) ab

= 35ab

v) 3x + (-7x) + 8x = (3 – 7 + 8) x^{2
}= (11 – 7) x^{2
}= 4x^{2}

vi) 4m” + 3m^{2 }+(-6m^{2}) + m^{2} = (4 + 3 – 6 + 1) m^{2
}= (8 – 6) m^{2
}= 2m^{2}

vii) 18pq + (-15 pq) + 3pq = (18 -15 + 3) pq

= (21 – 15) pq

= 6pq

Question 6.

Subtract the first term from the second term. (Page No. 200)

i) 2xy, 7xy

ii) 5a^{2}, 10a^{2}

iii) 12y, 3y

iv) 6x^{2}y, 4x^{2}y

v) 6xy, -12xy

Solution:

i) 2xy, 7xy

7xy – 2xy = (7 – 2) xy = 5xy

ii) 5a^{2}, 10a^{2
}10a -5a = (10-5) a^{2 }= 5a^{2}

iii) 12y, 3y

3y – 12y = (3 – 12)y = -9y

iv) 6x^{2}y, 4x^{2}y

4x^{2}y – 6x^{2}y = (4 – 6) x^{2}y = -2x^{2}y

v) 6xy,-12xy

(-12xy) – 6xy = (-12 – 6) xy = -18xy

Question 7.

Simplify the following. (Page No. 201)

i) 3m + 12m -5m

ii) 25yz – 8yz – 6yz

iii) 10m^{2} – 9m + 7m – 3m^{2
}iv) 9x^{2} – 6 + 4x + 11 – 6x^{2} – 2x + 3x^{2} – 2

v) 3a^{2} – 4a^{2}b + 7a^{2} – b^{2} – ab

vi) 5x^{2} + 10 + 6x + 4 + 5x + 3x^{2} + 8

Solution:

i) 3m + 12m -5m =(3+12-5)m

= (15 – 5) m

= 10m

ii) 25yz – 8yz – 6yz = (25 – 8 – 6) yz

= (25 – 14) yz

= 11 yz

iii) 10m^{2} – 9m + 7m – 3m^{2} – 5m – 8 = (10m^{2} – 3m^{2}) + (-9m + 7m – 5m) – 8

= (10 – 3)m^{2} + (-9 + 7 – 5) m – 8

= 7m^{2} + (-7m) – 8

= 7m^{2} – 7m – 8

iv) 9x^{2} – 6 + 4x + 11- 6x^{2} – 2x + 3x^{2} – 2

= (9x^{2}-6x^{2} + 3x^{2}) + (4x-2x) + (-6 + 11 -2)

= (9 – 6 + 3) x^{2} + (4 – 2) x + (11 – 8)

= (12 – 6) x^{2} + 2x + 3

= 6x^{2} + 2x + 3

v) 3a^{2} + 4a^{2}b – 7a^{2} – b^{2} – ab = (3a^{2} + 7a^{2}) – 4a^{2}b – b^{2} – ab

= 10a^{2} – b^{2} – 4a^{2}b – ab

vi) 5x^{2} + 10 + 6x + 4 + 5x + 3X^{2} + 8 = (5x^{2} + 3x^{2}) + (6x + 5x) + (10 + 4 + 8)

= 8x^{2} + 1 lx + 22

Question 8.

Write the following expressions in standard form. (Page No. 202)

Solution:

Expression – Standard form

i) 3x + 18 + 4x^{2} → 4x^{2} + 3x + 18

ii) 8 – 3x + 4x → -3x^{2} + 4x + 8

iii) -2m + 6 – 3m^{2 →} -3m^{2} – 2m + 6

iv) y^{3} + 1 + y + 3 → y^{3} + 3y^{2} + y + 1

Question 9.

Identify the expressions that are in standard form. (Page No. 202)

i) 9x^{2} + 6x + 8

ii) 9x^{2} + 15 + 7x

iii) 9x^{2} + 7

iv) 9x^{3} + 15x + 3

v) 15x^{2} + x^{3} + 3x

vi) x^{2}y + xy + 3

vii) x^{3 }+ x^{2}y^{2} + 6xy

Solution:

(i), (iii), (iv), (vi) are in standard form.

Question 10.

Write 5 different expressions in standard form. (Page No. 202)

Solution:

i) ax^{2} + bx + c

ii) ax + b

iii) 4x^{3} + 5x^{2} – 6x + 2

iv) 5x^{4} – 3x^{3} – 2x – 2

v) px^{3} + qx^{2} + r

Try This

Question 1.

Find the value of the expression ‘-9x’ if x = -3. (Page No. 203)

Solution:

The value of -9x when x = -3

-9x = -9 (-3) = + 27

Question 2.

Write an expression’ whose value is equal to -9, when x = -3. (Page No. 203)

Solution:

When x = -3, then the value of an expression 3x is -9.

∴ 3x = 3 (-3)= -9.

Do This

Question 1.

Answer the following expressions (Page No. 206)

i) x – 2y, 3x + 4y

ii) 4m^{2} – 7n^{2} + 5 mil, 3m^{2} + 5n^{2} – 2mn

iii) 3a – 4b, 5c – 7a + 2b

Solution:

i) x – 2y, 3x + 4y = (x – 2y) + (3x + 4y)

= (x + 3x) + (-2y + 4y) = 4x + 2y

ii) 4m^{2} – 7n^{2} + 5mn, 3m^{2} + 5n^{2} – 2mn = (4m^{2} – 7n^{2} + 5mn) + (3m^{2} + 5n^{2} – 2mn)

= (4m^{2} + 3m^{2}) + (-7n^{2} + 5n^{2}) + (5mn – 2mn)

= 7 m^{2} + (-2n^{2}) + 3mn = 7 m^{2} – 2n^{2} + 3mn

iii) 3a – 4b, 5c – 7a + 2b = (3a – 4b) + (5c – 7a + 2b) = (3a – 7a) + (-4b + 2b) + 5c = -4a – 2b + 5c