Let's solve the expression step-by-step:
The given expression is:
[tex]\[ 764 \times 66 + 764 \times 34 \][/tex]
First, observe that [tex]\( 764 \)[/tex] is a common factor in both terms of the expression. Therefore, we can factor out [tex]\( 764 \)[/tex] using the distributive property of multiplication over addition. The distributive property states that [tex]\( a(b + c) = ab + ac \)[/tex].
Applying this property to the given expression, we get:
[tex]\[ 764 \times 66 + 764 \times 34 = 764 \times (66 + 34) \][/tex]
Next, we need to add the numbers inside the parenthesis:
[tex]\[ 66 + 34 = 100 \][/tex]
Now our expression simplifies to:
[tex]\[ 764 \times 100 \][/tex]
Multiplying [tex]\( 764 \)[/tex] by [tex]\( 100 \)[/tex], we get:
[tex]\[ 764 \times 100 = 76400 \][/tex]
Thus, the value of the expression [tex]\( 764 \times 66 + 764 \times 34 \)[/tex] is:
[tex]\[ 76400 \][/tex]
Therefore, the correct answer is:
(d) 76400
