AP State Syllabus AP Board 8th Class Maths Solutions Chapter 11 Algebraic Expressions Ex 11.2 Textbook Questions and Answers.

## AP State Syllabus 8th Class Maths Solutions 11th Lesson Algebraic Expressions Exercise 11.2

Question 1.

Complete the table:

Solution:

Question 2.

Simplify: 4y(3y + 4)

Solution:

4y(3y + 4) = 4y × 3y + 4y × 4

= 12y^{2} + 6y

Question 3.

Simplify x(2x^{2} – 7x + 3) and find the values of it for (i) x = 1 and (ii) x = 0

Solution:

x(2x^{2} – 7x + 3)

= x × 2x^{2} – x × 7x + x × 3

= 2x^{3} – 7x^{2} + 3x

= 3 × 3 – 1 × 3 – 3 × 1 + 1 × 1

=9 – 3 – 3 + 1 = 4

∴(a – b)^{2} = 4sq.units

[∵ (3 – 1)^{2} = 2^{2} = 4]

(ii)

∴ (a – b)^{2} = a^{2} – 2ab + b^{2}

Area of ABCD + Area of CYZS

= a^{2} – 2ab + b^{2}

area of ABCD – area of BXYC – area of DCST + area of CYZS

= 5 × 5 – 2 × 5 – 2 × 5 + 2 × 2

= 25 – 10 – 10 + 4

= 9 sq.units

[∵ (5 – 2)^{2} = (3)^{2} = 9]

Question 4.

Add the product: a(a – b), b(b – c), c(c – a)

Solution:

a(a – b) + b(b – c) + c(c – a)

=a × a – a × b + b × b – b × c + c × c – c × a

=a^{2} – ab + b^{2} – bc + c^{2} – ca

=a^{2} + b^{2} + c^{2} – ab – bc – ca

Question 5.

Add the product: x(x + y – r), y(x – y+r), z(x – y – z)

Solution:

x(x + y – r) +y(x – y + r) + z(x – y – z)

= x^{2} + xy – xr + xy – y^{2} + yr + zx – yz – z^{2}

= x^{2} – y^{2} – z^{2} + 2xy – xr + yr + zx – yz

Question 6.

Subtract the product of 2x(5x – y) from product of 3x(x+2y)

Solution:

3x(x + 2y) – 2x(5x – y)

=(3x × x + 3x × 2y)-(2x × 5x – 2x × y)

= 3x^{2} + 6xy – (10x^{2} – 2xy)

= 3x^{2} + 6xy- 10x^{2} + 2xy

= 8xy – 7x^{2}

Question 7.

Subtract 3k(5k – l + 3rn) from 6k(2k + 3l – 2rn)

Solution:

6k(2k + 3l – 2m) – 3k(5k – l + 3m)

= 12k^{2}+ 18kl – 12km – 15k^{2} + 3kl – 9km

= -3k^{2} + 21kl – 21km

Question 8.

Simplify: a^{2}(a – b + c) + b^{2}(a + b – c) – c^{2}(a – b – c)

Solution:

a^{2}(a – b + c) + b^{2}(a + b – c) – c^{2}(a – b – c)

= a^{3} – a^{2}b + a^{2}c + ab^{2} + b^{3} – b^{2}c – ac^{2} + bc^{2} + c^{3}

= a^{3} + b^{3} + c^{3} – a^{2}b + a^{2}c + ab^{2} – b^{2}c – ac^{2} – bc^{2}