Factorize the following:
5(3a + b)² +6 (3a +b) - 8

[5(3a +b) - 4][ (3a +b) + 2]

Step-by-step explanation:

We can factorize the equation as follows:

5(3a + b)² +6 (3a +b) - 8 ..(1)

Let (3a +b) be y, therefore the question becomes

5y^2 + 6y - 8. (2)

Next, we have to multiply the first and last term together, and then find the factor such that the factors will result to 6. This is illustrated below:

5y^2 x - 8 = -40y^2

Factors of -40y^2 = 10y and - 4y

Substituting 10y and - 4y into the into equation (2) in place of 6y, we obtain:

5y^2 + 6y - 8

5y^2 + 10y - 4y - 8

Now, we factorize as follows:

5y(y + 2) - 4(y + 2)

Since we have same entity in both brackets, we shall pick one:

(5y - 4)(y + 2). (3)

But recall

y = (3a +b)

Substituting the value of y into equation (3), we have:

(5y - 4)(y + 2).

[ 5(3a +b) - 4 ][ (3a +b) + 2 ]

a

step-by-step explanation: