The DAV Class 8 Maths Solutions and **DAV Class 8 Maths Chapter 7 Worksheet 7 **Solutions of Algebraic Identities offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 7 WS 7 Solutions

Factorize the following:

Question 1.

x^{2} + 14x + 33

Solution:

x^{2} + 14x + 33 = x^{2} + 11x + 3x + 33

[By splitting the middle term]

= x (x + 11) + 3 (x + 11)

= (x + 11) (x + 3)

Question 2.

y^{2} – y – 6

Solution:

y^{2} – y – 6 = y^{2} – 3y + 2y – 6

[By splitting the middle term]

= y (y – 3) + 2 (y – 3)

= (y – 3) (y + 2)

Question 3.

x^{2} + x – 72

Solution:

x^{2} + x – 72 = x^{2} + 9x – 8x – 72

[Splitting the middle term]

= x (x + 9) – 8 (x + 9)

= (x + 9) (x – 8)

Question 4.

x^{2} + 12x + 27

Solution:

x^{2} + 12x + 27 = x^{2} + 9x + 3x + 27

[Splitting the middle term]

= x (x + 9) + 3 (x + 9)

= (x + 9) (x + 3)

Question 5.

y^{2} + y – 132

Solution:

y^{2} + y – 132 = y^{2} + 12y – 11y – 132

[Splitting the middle term]

= y (y + 12) – 11 (y + 12)

= (y + 12) (y – 11)

Question 6.

x^{2} + 11x + 30

Solution:

x^{2} + 11x + 30 = x^{2} + 6x + 5x + 30

[Splitting the middle term]

= x (x + 6) + 5 (x + 6)

= (x + 6) (x + 5)

Question 7.

x^{2} – 11z – 42 = x^{2} – 14x + 3x -42

[Splitting the middle term]

= x(x – 14) + 3(x – 14)

= (x – 14) (x + 3)

Question 8.

z^{2} – 12z + 27

Solution:

z^{2} – 12z + 27 = z^{2} – 3z – 9z + 12

[Splitting the middle term]

= z (z – 3) – 9 (z – 3)

= (z – 3) (z – 9)

Question 9.

p^{2} – 5p – 6

Solution:

p^{2} – 6 = p^{2} – 6p + p – 6

[Splitting the middle term]

= p (p – 6) + 1 (p – 6)

= (p – 6) (p + 1)

Question 10.

p^{2} + p – 56

Solution:

p^{2} + p – 56 = p^{2} + 8p – 7p -56

[Splitting the middle term]

= p (p +8) – 7(p + 8)

= (p + 8) (p – 7)

Question 11.

x^{2} – 8x – 65

Solution:

x^{2} – 8x – 65 = x^{2} – 13x + 5x -65

[Splitting the middle term]

= x (x – 13) + 5 (x – 13)

= (x – 13) (x + 5)

Question 12.

x^{2} + 8x + 15

Solution:

x^{2} + 8x + 15 = x^{2} + 3x + 5x + 15

[Splitting the middle term]

= x (x + 3) + 5 (x + 3)

= (x + 3) (x + 5)

Question 13.

x^{2} + 2x – 24

Solution:

x^{2} + 2x – 24 = x^{2} + 6x – 4x -24

[Splitting the middle term]

= x (x + 6) – 4 (x + 6)

= (x + 6) (x – 4)

Question 14.

x^{2} – 3x – 54

Solution:

x^{2} – 9x + 6x – 54

[Splitting the middle term]

= x (x – 9) + 6 (x – 9)

= (x – 9) (x + 6)

Question 15.

a^{2} – 7a + 12

Solution:

a^{2} – 7a + 12 = a^{2} – 4a – 3a + 12

= a (a – 4) – 3 (a – 4)

= (a – 4) (a – 3)

Question 16.

p^{2} – 3pq + 2q^{2}

Solution:

p^{2} – 3pq + 2q^{2} = p^{2} – 2pq – pq + 2q2^{2}

[Splitting the middle term]

= p (p – 2q) – q (p – 2q)

= (p – q) (p – 2q)

### DAV Class 8 Maths Chapter 7 Value Based Questions

Question 1.

In the vacations Gautam purchased (x^{2} + 8x – 20) game CDs, while Sanyam purchased (x + 4)^{2} game CDs.

(i) Who purchased more CDs and by how much?

(ii) Write any one advantage and one disadvantage of playing video games.

Solution:

(i) Number of game CDs purchased by Gautam = x^{2} + 8x – 20.

Number of game CDs purchased by Sanyam = (x + 4)^{2}

= x^{2} + 8x + 16.

Clearly, Sanyam purchased more CDs.

Difference = (x^{2} + 8x + 16) – (x^{2} + 8x – 20)

= x^{2} + 8x + 16 – x^{2} – 8x + 20 = 36.

(ii) Advantage – Entertainment

Disadvantage – Waste of time and money.

Question 2.

On the Earth Day, cubical flower pots (with plants) of base area (x^{2} + 6x + 9) square units were placed on a rectangular lane of area (x + 3) (7x + 21) square units.

(i) How many pots were placed?

(ii) Write the importance of trees in our life.

Solution:

(i) Base area of a cubical flower pot = x^{2} + 6x + 9

= x^{2} + 2 . x . 3 + (3)^{2}

= (x + 3)^{2}

Area of rectangular lane = (x + 3) (7x + 21)

= 7 (x + 3) (x + 3)

= 7 (x + 3)^{2}

Area of rectangular lane = (x + 3) (7x + 21)

= 7 (x + 3) (x + 3)

= 7 (x + 3)^{2}

∴ Number of pots = Area of rectangular lane Base area of a cubical flower pot / Base area of a cubical flower pot

= \(\frac{7(x+3)^2}{(x+3)^2}\) = 7.

(ii) Trees act as air purifier in our life.