a) The area of a rectangular football ground is $(2x^2 + 5x + 3)$ sq. units.

(i) Find the length and breadth of the ground.

(ii) Find the perimeter of the ground.

(iii) If $x = 46text{ m}$, find the actual perimeter of the ground.

b) The area of a rectangular garden is $(4x^2 + 8x + 3)$ sq. ft.

(i) Find the length and breadth of the garden.

(ii) If the length is increased by $5text{ ft.}$ and breadth is decreased by $2text{ ft.}$, find the new area of the garden.

Let’s factorise:

a) $a^2 + b^2 – c^2 – d^2 + 2ab – 2cd$

b) $p^2 + q^2 – r^2 – s^2 – 2pq – 2rs$

c) $a^2 – b^2 – 2bc – c^2$

d) $x^2 – y^2 + 2yz – z^2$

Let’s resolve into factors.

a) $2x^2 + 5xy + 2y^2$

b) $3x^2 + 5xy + 2y^2$

c) $2x^2 – xy – 3y^2$

d) $8x^2 + 2xy – 15y^2$

e) $15x^2 – 17xy – 4y^2$

f) $24a^2 – 38ab + 15b^2$

g) $15a^2 – 28ab + 12b^2$

h) $14a^2 – 38ab + 20b^2$

i) $8a^2 – 45ab – 18b^2$

Let’s resolve into factors.

a) $2x^2 + 5x + 3$

b) $2x^2 + 7x + 5$

c) $3x^2 + 8x + 4$

d) $3x^2 + 4x + 1$

e) $3x^2 + 5x + 2$

f) $3x^2 + 10x + 3$

g) $4x^2 + 12x + 5$

h) $4x^2 + 11x + 7$

i) $2x^2 – 3x + 1$

j) $3x^2 – 10x + 8$

k) $4x^2 – 8x + 4$

l) $8 – 22x + 9x^2$

m) $13 – 17x + 4x^2$

n) $6x^2 – 19x + 14$

o) $3a^2 – 20a + 17$

Let’s factorise.

a) $2x^2 + x – 3$

b) $3x^2 + x – 14$

c) $4x^2 + 5x – 6$

d) $5x^2 + 13x – 6$

e) $6x^2 + 11x – 2$

f) $7x^2 + 25x – 12$

g) $4x^2 + 4x – 3$

h) $6x^2 + 11x – 10$

i) $2a^2 – 5a – 12$

j) $3a^2 – 5a – 8$

k) $4a^2 – 16a – 9$

l) $2a^2 – 7a – 15$

m) $8x^2 – 22x – 21$

n) $6x^2 – 11x – 7$

o) $5x^2 – 13x – 6$

Let’s find the product and sum or difference of two numbers required for splitting the middle terms.

a) In $2x^2 + 3x + 1$: product of numbers = …….. and sum of numbers = ……..

b) In $3x^2 + 5x + 2$: product of numbers = …….. and sum of numbers = ……..

c) In $4x^2 – 8x + 3$: product of numbers = …….. and sum of numbers = ……..

d) In $5x^2 – 12x + 4$: product of numbers = …….. and sum of numbers = ……..

e) In $2x^2 + 5x – 3$: product of numbers = …….. and difference of numbers = ……..

f) In $3x^2 + 2x – 8$: product of numbers = …….. and difference of numbers = ……..

Let’s write the following expressions as the product of their factors.

a) $2x(x + 1) + 1(x + 1) =$ ………………..

b) $2x(x – 1) – 1(x – 1) =$ ………………..

c) $3x(2x + 1) + 2(2x + 1) =$ ………………..

d) $3x(2x – 1) – 2(2x – 1) =$ ………………..

e) $2x(3x – 2) + (3x – 2) =$ ………………..

f) $2x(3x + 2) + (3x + 2) =$ ………………..

a) The area of a rectangle is $a^2 + 6a + 8$ sq. units. Find its length and breadth. Also find the perimeter of the rectangle.

b) The area of a rectangular ground is $x^2 + 5x – 36$ sq. unit. If its length and breadth are reduced by 2/2 unit, find the new area of the ground.

Let’s factorise.

a) $x^3 + 15x^2 + 56x$

b) $x^3 + 17x^2 + 42x$

c) $x^4 – 4x^3 – 21x^2$

d) $x^4 – 14x^3 + 45x^2$

e) $x^3 + 13x^2 – 30x$

f) $x^4 + 2x^3 – 8x^2$

g) $x^5 – 18x^4 + 72x^3$

h) $x^5 + 11x^4 – 102x^3$

Let’s factorise.

a) $(x + y)^2 + 5(x + y) + 6$

b) $(a + b)^2 + 14(a + b) + 33$

c) $(p – q)^2 – 11(p – q) + 30$

d) $(x – y)^2 – 9(x – y) – 22$