Question

How do you find the product $\left( 3c-5 \right)\left( c+5 \right)$?

Answer 1

Hint: To solve the given equation we will first use distributive property. Now we will again use distributive property to open the brackets of the obtained equation. Now we will multiply the term of the equation and hence find the product of the given equation.

Complete step-by-step solution:
To find the product first we will understand the commutative, associative and distributive property.
Now commutative property of addition states that a + b = b + a.
Similarly commutative property of multiplication states that a.b = b.a.
Now associative property of addition is a + (b + c) = (a + b) + c
Similarly the associative property of multiplication states that a(b.c) = (a.b)c.
Now let us understand the distributive property of multiplication.
According to this property we distribute the multiplied term over addition or subtraction.
Hence we have $a.\left( b+c \right)=a.b+a.c$
Similarly $a.\left( b-c \right)=a.b-a.c$
Now we use these properties to simplify expressions.
Now consider the given equation $\left( 3c-5 \right)\left( c+5 \right)$
Now we know that according to distributive property we have,
$\Rightarrow \left( 3c-5 \right)\left( c+5 \right)=3c\left( c+5 \right)-5\left( c+5 \right)$
Now again we will use distributive property and open the brackets.
$\Rightarrow 3c\left( c \right)+3c\left( 5 \right)-5\left( c \right)-5\left( 5 \right)$
Now multiplying the terms we get.
$\Rightarrow 3{{c}^{2}}+15c-5c-25$
Now again using the distributive property we know that $\left( 15-5 \right)c=15c-5c$. Hence using this we get,
$\Rightarrow 3{{c}^{2}}+\left( 15-5 \right)c-25$
$\Rightarrow 3{{c}^{2}}+10c-25$
Hence the product of the terms $\left( 3c-5 \right)\left( c+5 \right)$ is $3{{c}^{2}}+10c-25$.

Note: Now note that according to distributive property we have $a\left( b+c \right)=a.b+a.c$. To solve $\left( 3c-5 \right)\left( c+5 \right)$ we will first consider $\left( c+5 \right)$ as one term. Hence we distribute the term as $\left( c+5 \right)\left( 3c \right)-5\left( c+5 \right)$ . Also note that we can use distributive property from the left side as well as right side. For example $a\left( b-c \right)=\left( b-c \right)a=ab-ac$ . Also we can directly add the terms of the same degree and hence we can directly say that 15c + 5c = 20c.