The property that is illustrated by the statement 150 × (-30 + 63) = 150 × -30 + 150 × 63 is the Distributive property of multiplication over addition.
To understand why, let's break down each side of the equation:
On the left side, we have 150 × (-30 + 63). This represents the multiplication of 150 by the result of the operation inside the parenthesis, which is the addition of -30 and 63.
On the right side, we have 150 × -30 + 150 × 63. This represents the sum of the two products: 150 multiplied by -30 and 150 multiplied by 63.
The equality of these two expressions demonstrates the Distributive property of multiplication over addition. This property says that multiplying a number by the sum of two other numbers gives the same result as multiplying that number by each of the two other numbers individually and then adding those products together.
So, the correct answer is option 'b': Distributive property of multiplication over addition.