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Simplify the following using brackets. ...

Simplify the following using brackets.
`36 xx 48`

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To simplify the expression \( 36 \times 48 \) using brackets, we can follow these steps: ### Step-by-Step Solution: 1. **Rewrite the Numbers**: We can express 36 and 48 in terms of a common number. Let's write: \[ 36 = 50 - 14 \quad \text{and} \quad 48 = 50 - 2 \] So, we can rewrite the expression as: \[ 36 \times 48 = (50 - 14) \times (50 - 2) \] 2. **Use the Formula**: We can use the formula for the product of two binomials, which is: \[ (x - a)(x - b) = x^2 - (a + b)x + ab \] Here, \( x = 50 \), \( a = 14 \), and \( b = 2 \). 3. **Substitute Values into the Formula**: Now we substitute the values into the formula: \[ (50 - 14)(50 - 2) = 50^2 - (14 + 2) \times 50 + (14 \times 2) \] 4. **Calculate Each Part**: - Calculate \( 50^2 \): \[ 50^2 = 2500 \] - Calculate \( a + b \): \[ 14 + 2 = 16 \] - Calculate \( ab \): \[ 14 \times 2 = 28 \] 5. **Combine the Results**: Now, substitute these values back into the expression: \[ 2500 - 16 \times 50 + 28 \] - Calculate \( 16 \times 50 \): \[ 16 \times 50 = 800 \] - Now substitute this back: \[ 2500 - 800 + 28 \] 6. **Final Calculation**: - First, subtract \( 800 \) from \( 2500 \): \[ 2500 - 800 = 1700 \] - Then, add \( 28 \): \[ 1700 + 28 = 1728 \] ### Final Answer: Thus, the simplified result of \( 36 \times 48 \) is: \[ \boxed{1728} \]
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