Which of the following is not true?
\( (7+8)+9 = 7+(8+9) \)
\( (7 imes8) imes9 = 7 imes(8 imes9) \)
\( 7 + 8 imes9 = (7+8) imes(7+9) \)
\( 7 imes(8+9) = (7 imes8)+(7 imes9) \)
Option A: \((7+8)+9 = 7+(8+9)\) is true because it follows the associative property of addition, which states that the way numbers are grouped does not change the sum: \((a+b)+c = a+(b+c)\).
Option B: \((7\times8)\times9 = 7\times(8\times9)\) is true due to the associative property of multiplication, which allows changing the grouping of factors without affecting the product: \((a\times b)\times c = a\times(b\times c)\).
Option C: \((7 + 8\times9) = (7+8)\times(7+9)\) is not true because no property of real numbers (associative, commutative, or distributive) allows converting an expression of the form \(a + b\,c\) into a product like \((a+b)(a+c)\). By comparing the general algebraic forms, the left side \(a + bc\) is linear, while the expanded right side \((a+b)(a+c) = a^2 + a(b+c) + bc\) contains an \(a^2\) term. These expressions are structurally different, so they cannot be equal in general. Therefore, Option C is the one that is not true.
Option D: \(7\times(8+9) = (7\times8)+(7\times9)\) is true because it directly uses the distributive property: \(a(b+c) = ab + ac\).