If a + b =3 and ab = 5, then what is the value of the expression (1 + a) (1 + b)? (a). 9 (b). 8 (c). -9 (d). 6
Hint: For a quicker answer instead of finding the values of a and using the given conditions multiply the brackets given in the required expression , then substitute the given values.
Complete step-by-step answer: It is given that a + b = 3 and ab = 5. The value of the required expression = (1 + a) (1 + b)………….(1)
When expanding double brackets, every term in the first bracket has to be multiplied by every term in the second bracket. It is helpful to always multiply the terms in order so none are forgotten. One common method used is FOIL: First, Outside, Inside, Last. Expand the brackets (1 + a) (1 + b).
Multiply the first items in the brackets: $1\times 1=1$
Multiply the terms that are on the outsides of the brackets: $1\times b=b$
Multiply the terms on the insides of the brackets: $a\times 1=a$
Multiply the last terms in the brackets: $a\times b=ab$
This gives: 1+ b + a + ab
The equation (1) becomes
The value of the required expression = (1 + a) (1 + b)
The value of the required expression = 1+ b + a + ab
The value of the required expression = 1+ (a + b)+ ab
Put the value a + b =3 and ab = 5, we get
The value of the required expression = 1+ (3) + (5)
The value of the required expression = 9
Therefore, the correct option is (a).
Note: The longer approach to the solution is to find the values of a and b separately using the two given expressions and then substitute their value in the required expression for the final answer.