Answer :
Sure, let's verify the expression \( a + (b + c)(a + b + c) \) for \( a = 15 \), \( b = 20 \), and \( c = 30 \).
1. Step 1: Calculate \( b + c \)
[tex]\[ b + c = 20 + 30 = 50 \][/tex]
So, \( b + c = 50 \).
2. Step 2: Calculate \( a + b + c \)
[tex]\[ a + b + c = 15 + 20 + 30 = 65 \][/tex]
So, \( a + b + c = 65 \).
3. Step 3: Substitute \( b + c \) and \( a + b + c \) into the expression
The given expression is:
[tex]\[ a + (b + c)(a + b + c) = 15 + (50 \cdot 65) \][/tex]
4. Step 4: Compute \( 50 \cdot 65 \)
[tex]\[ 50 \cdot 65 = 3250 \][/tex]
So, we have:
[tex]\[ a + (3250) = 15 + 3250 \][/tex]
5. Step 5: Add \( 15 \) to \( 3250 \)
[tex]\[ 15 + 3250 = 3265 \][/tex]
Thus, the value of the expression [tex]\( a + (b + c)(a + b + c) \)[/tex] for [tex]\( a = 15 \)[/tex], [tex]\( b = 20 \)[/tex], and [tex]\( c = 30 \)[/tex] is [tex]\( \boxed{3265} \)[/tex].
1. Step 1: Calculate \( b + c \)
[tex]\[ b + c = 20 + 30 = 50 \][/tex]
So, \( b + c = 50 \).
2. Step 2: Calculate \( a + b + c \)
[tex]\[ a + b + c = 15 + 20 + 30 = 65 \][/tex]
So, \( a + b + c = 65 \).
3. Step 3: Substitute \( b + c \) and \( a + b + c \) into the expression
The given expression is:
[tex]\[ a + (b + c)(a + b + c) = 15 + (50 \cdot 65) \][/tex]
4. Step 4: Compute \( 50 \cdot 65 \)
[tex]\[ 50 \cdot 65 = 3250 \][/tex]
So, we have:
[tex]\[ a + (3250) = 15 + 3250 \][/tex]
5. Step 5: Add \( 15 \) to \( 3250 \)
[tex]\[ 15 + 3250 = 3265 \][/tex]
Thus, the value of the expression [tex]\( a + (b + c)(a + b + c) \)[/tex] for [tex]\( a = 15 \)[/tex], [tex]\( b = 20 \)[/tex], and [tex]\( c = 30 \)[/tex] is [tex]\( \boxed{3265} \)[/tex].
