Question

Multiply the following algebraic expression: $ \left( {x + 3} \right)\left( {x + 4} \right) $

Answer 1

Hint: We are given an algebraic expression and we have to simply solve this by multiplying the expression which is in factored form to reach the quadratic form. So we multiply one variable by all others one by one and then combine terms to write the final answer.

Complete step-by-step answer:
Firstly we write down the algebraic expression given in the question
 $ \left( {x + 3} \right)\left( {x + 4} \right) $
The expression only has one variable and if we closely observe it we can see that it is in the factored form of algebraic expressions i.e.
 $ {x^2} + \left( {a + b} \right)x + ab = \underbrace {\left( {x + a} \right)\left( {x + b} \right)}_{{\text{Factorized}}\,{\text{Form}}} $ ----equation (1)
So we have to convert it into the quadratic form of algebraic expression i.e. after multiplication we have to expand it in quadratic form so we either use the above equation (1) formula or we multiply it conventionally.
When we multiply it conventionally we take the first element of the first factor and multiply it with all elements of other factor then take the second element and multiply it with all elements of other factor and repeat the process. Understanding it by this mathematical expression where on top of expressions represents the numbers operated upon.
 $ {x^2} + \left( {a + b} \right)x + ab = \left( {x + a} \right)\left( {x + b} \right) $
it means we have $ a = 3\,{\text{and}}\,b = 4 $ , so we have
 $ (x + 3)(x + 4) = {x^2} + (3 + 4)x + 3 \times 4 = {x^2} + 7x + 12 $
So we have multiplied the factors and obtained the result.
So, the correct answer is “ $ {x^2} + 7x + 12 $ ”.

Note: We used the basic multiplication method because we had to find multiplication in the question. If we were asked to solve the expression then a more appropriate solution would have been the formula method of factorization expressions provided by equation (1).