Question

Give possible expressions for the length and breadth of the rectangle whose area is given
by (i) 4a2 + 4a − 3 (ii) 25a2 − 35a + 12

Answer 1

Explanation:

4a²+4a-3

4a²+6a-2a -3

2a(2a+3)-1(2a+3)

(2a-1)(2a+3)

length =(2a-1),breadth= (2a+3)

2.25a²-35a+12

25a²-20a-15a+12

5a(5a-4)-3(5a-4)

(5a-3)(5a-4)

length =5a-3

breadth =5a-4

Answer 2

hi mate,

solution:

Factoring 4a²+4a-3

4a² - 2a + 6a - 3

Step-1 : Add up the first 2 terms, pulling out like factors :

2a • (2a-1)

Add up the last 2 terms, pulling out common factors :

3 • (2a-1)

Step-2 : Add up the four terms of step 1 :

(2a+3) • (2a-1)

Which is the desired factorization

Final result :

(2a - 1) • (2a + 3)

length = (2a - 1) and breadth = (2a + 3)

or a = 1/2 and a = 3/2

and

Factoring 25a²-35a+12

25a² - 20a - 15a - 12

Step-1 : Add up the first 2 terms, pulling out like factors :

5a • (5a-4)

Add up the last 2 terms, pulling out common factors :

3 • (5a-4)

Step-2 : Add up the four terms of step 1 :

(5a-3) • (5a-4)

Which is the desired factorization

Final result :

(5a - 4) • (5a - 3)

length = (5a - 4) and breadth = (5a - 3)

or a = 4/5 and a = 3/5

i hope it helps you.