Looking at the diagram, we can write an expression that represents the total area of the rectangle.
7x+49
Recall that an algebraic expression is in factored form when it is expressed as the product of its factors. We can write the expression that we got in factored form using the greatest common factor (GCF). Let's start by writing the prime factorization of 7 and 49x.
rcl
7 & = & 7 [0.2em]
49x & = & 7 * 7 * x
The GCF of 7 and 49x is the product of the prime factors that are common to these monomials.
rcl
7 & = & 7 [0.2em]
49x & = & 7 * 7 * x [0.5em]
GCF & = & 7
We got that the GCF of 7 and 49x is 7. Next, we will write each monomial as a product of the GCF and its remaining factors and use the Distributive Property to factor out the GCF.
7+49x = 7 * 1 + 7 * 7x = 7(1 + 7x)
The total area of the rectangle, written in factored form, is equal to 7(1+7x) square units.
