To solve the mathematical expression [tex]\( 17 \times 38 + 17 \times 12 \)[/tex], we can use the distributive property of multiplication over addition. This property states that for any numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex],
[tex]\[ a \times b + a \times c = a \times (b + c) \][/tex]
In this case, [tex]\(a = 17\)[/tex], [tex]\(b = 38\)[/tex], and [tex]\(c = 12\)[/tex].
Following the steps:
1. Identify the common factor: Notice that 17 is common in both terms of the expression.
[tex]\[ 17 \times 38 + 17 \times 12 \][/tex]
2. Factor out the common term: Factor 17 out of the expression.
[tex]\[ 17 \times (38 + 12) \][/tex]
3. Sum the terms inside the parentheses: Add the numbers inside the parentheses.
[tex]\[ 38 + 12 = 50 \][/tex]
4. Multiply the factor by the summed terms: Multiply 17 by the result of the addition.
[tex]\[ 17 \times 50 \][/tex]
5. Calculate the final result: Perform the multiplication.
[tex]\[ 17 \times 50 = 850 \][/tex]
Thus, the value of the expression [tex]\( 17 \times 38 + 17 \times 12 \)[/tex] is [tex]\( 850 \)[/tex].
