Question

1. make sense and persevere write a numerical expression, with at least three operations, that has the same value as ((12 - 9)^2\times(4 + 3)). justify your answer.

Explanation:

Step1: Calculate target value

First compute the given expression:
$$(12-9)^2 \times (4+3) = 3^2 \times 7 = 9 \times 7 = 63$$

Step2: Build equivalent expression

Create an expression with ≥3 operations that equals 63. Example:
$$(5 + 2) \times 10 - 7 + 0$$
Verify: $7 \times 10 -7 +0 = 70 -7 +0 = 63$

Step3: Justify the equivalence

Confirm the new expression simplifies to 63, matching the target value.

Answer:

One valid numerical expression is $\boldsymbol{(5 + 2) \times 10 - 7 + 0}$.

Justification:

1. The original expression $(12-9)^2 \times (4+3)$ simplifies to $3^2 \times 7 = 9 \times 7 = 63$.
2. The new expression simplifies as follows: $(5+2)=7$, $7 \times 10=70$, $70-7=63$, $63+0=63$. Both expressions evaluate to 63, so they are equivalent, and it uses addition, multiplication, subtraction, and addition (four total operations, meeting the "at least three" requirement).