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Evaluate: $(c + 5)(c - 3)$.

Last updated date: 19th Mar 2023
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Hint: It is a simple algebraic expression. we can solve this either by directly using the algebraic formula $(a + b)(a - c) = {a^2} + a(b - c) - bc$ to obtain the final expression or we can simplify the given expression by multiplying the terms to get the required expression.

Given: $(c + 5)(c - 3)$
It can be written as
$c(c - 3) + 5(c - 3)$
By further calculation
${c^2} - 3c + 5c - 15$
on simplification
${c^2} + 2c - 15$
Further if you simplify the obtained expression by taking the common factor, we will get back the given expression that the obtained solution is ${c^2} + 2c - 15$. Simplifying the above using factorization method we get factors as $5$ and $- 3$ with this above expression can be written as ${c^2} + 5c - 3c - 15$. Taking common factor and rearranging
$c(c + 5) - 3(c + 5)$
Again, taking common factor we get
$(c + 5)(c - 3)$

Note: the given expression is of the form $(a + b)(a - b)$so we can directly use the formula
$(a + b)(a - c) = {a^2} + a(b - c) - bc$
Where $a = c,b = 5,c = 3$
on substitution in the above formula we get,
$(c + 5)(c - 3) = {c^2} + c(5 - 3) - (5)(3)$
$\Rightarrow {c^2} + 5c - 3c - 15$
$\Rightarrow c(c + 5) - 3(c + 5)$
Further if you simplify the obtained expression by taking the common factor, we will get back the given expression that the obtained solution is ${c^2} + 2c - 15$. Simplifying the above using factorization method we get factors as $5$ and $- 3$ with this above expression can be written as ${c^2} + 5c - 3c - 15$. (taking common factor and rearranging)
$c(c + 5) - 3(c + 5)$
Again, taking common factor we get,
$(c + 5)(c - 3)$
The solution is the same in both cases. In the above problem we cannot simplify the equation further to get the value of c because the given expression is not equated to zero. (that is supposed if the given equation is of the form $(c + 5)(c - 3) = 0$ then we can simplify it by using Factorization method or formula method).