Answer: 17
Step-by-step explanation:
Given: [tex](ax+b)(2x+3)=20x^2+44x+21[/tex], where a and b are two distinct integers.
First simplify left hand side as
[tex](ax+b)(2x+3)=ax\cdot \:2x+ax\cdot \:3+b\cdot \:2x+b\cdot \:3\\\\=2axx+3ax+2bx+3b\\\\=2ax^2+(3a+2b)x+3b[/tex]
Then comparing left side and right side
[tex]2ax^2+(3a+2b)x+3b=20x^2+44x+21[/tex]
we get 2a = 20 (coefficient of [tex]x^2[/tex]) , and 3b = 21 (constant term)
⇒ a= 10 and b= 7
Then, a+b= 10+7=17
Hence, the value of sum a+b is 17.
