Question

evaluate the expression $4 \cdot 3 - (9 - 7)^2 + 6$. next, evaluate the multiplication. $4 \cdot 3 - (9 - 7)^2 + 6 = 4 \cdot 3 - 2^2 + 6 = \square \cdot \square - \square + 6$

Explanation:

Step1: Evaluate multiplication (4·3)

First, calculate the multiplication \(4 \cdot 3\). By the basic multiplication operation, \(4 \times 3 = 12\). Then, evaluate the exponent \(2^2\). By the definition of exponentiation, \(2^2 = 4\). So the expression becomes \(12 - 4 + 6\) at this step (but for the blanks, we just need the result of multiplication and the exponent result). Wait, the problem is about filling the blanks: the first blank is the multiplication \(4 \cdot 3\) result, and the second blank is \(2^2\) result. Wait, no, the current step is "evaluate the multiplication" and then the exponent? Wait, the expression after simplifying the parentheses is \(4 \cdot 3 - 2^2 + 6\). Now, evaluating the multiplication: \(4 \cdot 3 = 12\), and evaluating the exponent \(2^2 = 4\). So the blanks should be 12 (for the multiplication part) and 4 (for the exponent part). Wait, the first blank is \(4 \cdot 3\) which is 12, and the second blank is \(2^2\) which is 4. Let's check:

Original step: \(4 \cdot 3 - (9 - 7)^2 + 6 = 4 \cdot 3 - 2^2 + 6\)

Then, "evaluate the multiplication" (4·3) gives 12, and evaluate the exponent (2²) gives 4. So the next line is \(12 - 4 + 6\). So the first blank (the multiplication result) is 12, and the second blank (the exponent result) is 4. Wait, the first box is "□ · □" but no, wait the first box is "□ · □" but actually, the first box is the result of \(4 \cdot 3\), which is 12? Wait, no, the first box is written as "□ · □" but that's a typo? Wait, no, looking at the image: the first box is "□ · □" but actually, after evaluating the multiplication, \(4 \cdot 3 = 12\), so the first box is 12 (but the format is "□ · □" which is confusing). Wait, no, maybe the first box is the multiplication part, so \(4 \cdot 3 = 12\), so the first box is 12 (but the dot is there, maybe it's a mistake, and the first box is 12, and the second box is \(2^2 = 4\). Let's confirm:

The expression after parentheses: \(4 \cdot 3 - 2^2 + 6\)

Now, evaluate the multiplication: \(4 \cdot 3 = 12\), so replace \(4 \cdot 3\) with 12. Then evaluate the exponent: \(2^2 = 4\), so replace \(2^2\) with 4. So the next line is \(12 - 4 + 6\). Therefore, the first blank (the multiplication result) is 12 (so the first box is 12, with the dot, maybe it's a formatting error, and the first box is 12, and the second box is 4.

Step1: Evaluate \(4 \cdot 3\)

\(4 \cdot 3 = 12\)

Step2: Evaluate \(2^2\)

\(2^2 = 4\)

So the first blank (multiplication) is 12, the second blank (exponent) is 4.

Answer:

The first blank (multiplication result) is 12, the second blank (exponent result) is 4. So the filled line is \(12 - 4 + 6\). So the first box is 12 (for \(4 \cdot 3\)) and the second box is 4 (for \(2^2\)).