DAV Class 8 Maths Chapter 7 Worksheet 7 Solutions

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.
x² + 14x + 33
Solution:
x² + 14x + 33 = x² + 11x + 3x + 33
[By splitting the middle term]
= x (x + 11) + 3 (x + 11)
= (x + 11) (x + 3)

Question 2.
y² – y – 6
Solution:
y² – y – 6 = y² – 3y + 2y – 6
[By splitting the middle term]
= y (y – 3) + 2 (y – 3)
= (y – 3) (y + 2)

Question 3.
x² + x – 72
Solution:
x² + x – 72 = x² + 9x – 8x – 72
[Splitting the middle term]
= x (x + 9) – 8 (x + 9)
= (x + 9) (x – 8)

Question 4.
x² + 12x + 27
Solution:
x² + 12x + 27 = x² + 9x + 3x + 27
[Splitting the middle term]
= x (x + 9) + 3 (x + 9)
= (x + 9) (x + 3)

Question 5.
y² + y – 132
Solution:
y² + y – 132 = y² + 12y – 11y – 132
[Splitting the middle term]
= y (y + 12) – 11 (y + 12)
= (y + 12) (y – 11)

Question 6.
x² + 11x + 30
Solution:
x² + 11x + 30 = x² + 6x + 5x + 30
[Splitting the middle term]
= x (x + 6) + 5 (x + 6)
= (x + 6) (x + 5)

Question 7.
x² – 11z – 42 = x² – 14x + 3x -42
[Splitting the middle term]
= x(x – 14) + 3(x – 14)
= (x – 14) (x + 3)

Question 8.
z² – 12z + 27
Solution:
z² – 12z + 27 = z² – 3z – 9z + 12
[Splitting the middle term]
= z (z – 3) – 9 (z – 3)
= (z – 3) (z – 9)

Question 9.
p² – 5p – 6
Solution:
p² – 6 = p² – 6p + p – 6
[Splitting the middle term]
= p (p – 6) + 1 (p – 6)
= (p – 6) (p + 1)

Question 10.
p² + p – 56
Solution:
p² + p – 56 = p² + 8p – 7p -56
[Splitting the middle term]
= p (p +8) – 7(p + 8)
= (p + 8) (p – 7)

Question 11.
x² – 8x – 65
Solution:
x² – 8x – 65 = x² – 13x + 5x -65
[Splitting the middle term]
= x (x – 13) + 5 (x – 13)
= (x – 13) (x + 5)

Question 12.
x² + 8x + 15
Solution:
x² + 8x + 15 = x² + 3x + 5x + 15
[Splitting the middle term]
= x (x + 3) + 5 (x + 3)
= (x + 3) (x + 5)

Question 13.
x² + 2x – 24
Solution:
x² + 2x – 24 = x² + 6x – 4x -24
[Splitting the middle term]
= x (x + 6) – 4 (x + 6)
= (x + 6) (x – 4)

Question 14.
x² – 3x – 54
Solution:
x² – 9x + 6x – 54
[Splitting the middle term]
= x (x – 9) + 6 (x – 9)
= (x – 9) (x + 6)

Question 15.
a² – 7a + 12
Solution:
a² – 7a + 12 = a² – 4a – 3a + 12
= a (a – 4) – 3 (a – 4)
= (a – 4) (a – 3)

Question 16.
p² – 3pq + 2q²
Solution:
p² – 3pq + 2q² = p² – 2pq – pq + 2q2²
[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 (x² + 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 = x² + 8x – 20.
Number of game CDs purchased by Sanyam = (x + 4)²
= x² + 8x + 16.
Clearly, Sanyam purchased more CDs.
Difference = (x² + 8x + 16) – (x² + 8x – 20)
= x² + 8x + 16 – x² – 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 (x² + 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 = x² + 6x + 9
= x² + 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.