1. Factorization by
identity (x + a)(x + b)

2. 1. Factorize the following expression by using an identity.
x² + 7x + 12
12 is not a square of any number , so we cannot use the identity a² + 2ab + b²
x² x
x2 + (a + b)x + ab = (x + a) (x + b)
So we need to find value of a and b, such that a + b = 7 and ab = 12 a b
a + b ab
a+b=7
ab=12
choice 1 6 7 6
yes no 2 5 7 10
yes no 3 4 7 12
yes
yes
We take a=3 and b=4 since we get a + b = 7 and ab = 12
Now we can factorize x² + 7x using x2 + (a + b)x + ab = (x + a) (x + b) identity
x² + 7x = (x + 3) (x + 4) Substituting a = 3 and b = 4 in (x + a) (x + b)
Ans : x² + 7x + 12= (x + 3) (x + 4)

3. 2. Factorize the following expression by using an identity.
x² - 3x - 4
-4 is not a square of any number , so we cannot use the identity a² + 2ab + b²
x² x
x2 + (a + b)x + ab = (x + a) (x + b)
So we need to find value of a and b, such that a + b = -3 and ab = -4 a b
a + b ab
a+b=-3
ab=-4
choice -1 3 2 -3 no no 2 -2 -4 no
yes 1 -4 -3 -4
yes
yes
We take a=1 and b= -4 since we get a + b = -3 and ab = -4
Now we can factorize x² - 3x - 4 using x2 + (a + b)x + ab = (x + a) (x + b) identity
x² - 3x - 4 = (x + 1) (x - 4) Substituting a =1 and b = -4 in (x + a) (x + b)
Ans : x² - 3x - 4 = (x + 1) (x - 4)

4. = 15x2 -10 x + 6x -4 rewriting term -4x as ‘-10x + 6x’
3 Factorize the following expression by using an identity.
15x² - 4x -4
27 is not a square of any number , so we cannot use the identity a² + 2ab + b²
15x² - 4x
We have leading coefficient 15 and it is not of the form x2 + (a + b)x + ab
We need to split the numerical coefficient of middle term -4 into two values a and b
such that a + b = -4 and ab = -4 x ‘leading coefficient’ i.e ab=-4 x 15 = -60 a b
a + b ab
a+b=-4
ab=-60
choice no 1
-60
-59
-60 ye no 2
-30
-15
-60
yes no 3
-20
-17
-60
yes 4
-15
-11
-60 no
yes 6
-10 -4
-60
yes
yes
We take a=6 and b= -10 since we get a + b = -4 and ab = -60
15x2 -4x - 4
= 15x x + 6x -4 rewriting term -4x as ‘-10x + 6x’
by taking out common factor 5x in group 1
=5x(3x-2)
+2(3x-2)
by taking out common factor 2 in group 2
=(5x + 2)(3x-2) by taking out common factor (3x-2)

5. Try These Factorize the following expression by using identities :
x2 +7x + 10
y2 + y - 20