Question

Сократите выражение, используя короткую формулу умножения: (1/2y-1/3x) (1/3x + 1/2y) помогите у нас соч

Answer 1

$\displaystyle\bf\\\Big(\frac{1}{2} y-\frac{1}{3} x\Big)\Big(\frac{1}{3} x+\frac{1}{2} y\Big)=\Big(\frac{1}{2}y\Big)^{2} -\Big(\frac{1}{3} x\Big)^{2} =\frac{1}{4}y^{2} } -\frac{1}{9} x^{2}$

При решении была применена формула разности квадратов :

$\displaystyle\bf\\\boxed{\boxed{(a-b)(a+b)=a^{2} -b^{2} }}$

Answer 2

Simplifying the Expression:

To simplify the given expression using the short multiplication formula, we can use the following steps:

1. Identify the Expression: The given expression is (1/2y - 1/3x) + (1/3x + 1/2y).

2. Apply the Short Multiplication Formula: We can simplify the expression by recognizing that the terms 1/3x and 1/3x cancel each other out, as do the terms 1/2y and 1/2y.

3. Simplified Expression: After applying the short multiplication formula, the simplified expression is 1/2y - 1/3x + 1/3x + 1/2y.

4. Final Simplified Expression: By canceling out the like terms, the final simplified expression is 1y.

Therefore, the simplified form of the given expression using the short multiplication formula is 1y.

Explanation:

The given expression (1/2y - 1/3x) + (1/3x + 1/2y) can be simplified using the short multiplication formula. By recognizing that the terms 1/3x and 1/3x cancel each other out, as do the terms 1/2y and 1/2y, we can simplify the expression to 1y.

This simplification is based on the cancellation of like terms, resulting in the final simplified expression of 1y.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.