Example Question - solving expression
Here are examples of questions we've helped users solve.
Solving an Expression with Sum of Cubes
The image is rotated; I'll provide the steps to reach the solution as if the image were in the correct orientation. Given: a^2/b + b^2/a = ? To find the above expression, we combine the terms over a common denominator: Step 1: a^2/b + b^2/a = (a^3 + b^3) / (ab) Then, by applying the sum of cubes formula a^3 + b^3 = (a + b)(a^2 - ab + b^2), we simplify the expression: Step 2: (a^3 + b^3) / (ab) = [(a + b)(a^2 - ab + b^2)] / (ab) Finally, we factor out a from the first term and b from the second term in the numerator: Step 3: [(a + b)(a^2 - ab + b^2)] / (ab) = (a + b)(a - b + b) / b + (a + b)(a + a - b) / a This simplifies to: Step 4: (a + b)(a) / b + (a + b)(b) / a Now we split the terms to simplify further: Step 5: a(a + b) / b + b(a + b) / a Separate the terms: Step 6: a^2/b + ab/b + ab/a + b^2/a Further simplification: Step 7: a^2/b + a + a + b^2/a Combine like terms: Step 8: a^2/b + 2a + b^2/a And if required to write as a single fraction: Step 9: (a^3 + 2a^2b + b^3) / ab This represents the expression in terms of a single fraction, but the final simplified form is as mentioned in step 8: Final Answer: a^2/b + 2a + b^2/a
Solving Expression using Distributive Property and Combining Like Terms
To solve the expression given in the image, you'll need to apply the distributive property and combine the like terms. The expression is: \(-6x^2(3x^5)\) When multiplying two exponential expressions with the same base, you add the exponents: \(x^2 \cdot x^5 = x^{2+5} = x^7\) Now multiply the coefficients, which are the numerical parts: \(-6 \cdot 3 = -18\) Combining both parts, you get: \(-18x^7\) So the simplified expression is: \(-18x^7\)
Solving Expression with Reciprocal
To solve the expression x + \(\frac{1}{x}\) given that \(x = 2 + \sqrt{3}\), first find the reciprocal of x and then add it to x. Given \(x = 2 + \sqrt{3}\), the reciprocal, \(\frac{1}{x}\), can be calculated as follows: \[ \frac{1}{x} = \frac{1}{2 + \sqrt{3}} \] To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator: \[ \frac{1}{x} = \frac{1}{2 + \sqrt{3}} \cdot \frac{2 - \sqrt{3}}{2 - \sqrt{3}} = \frac{2 - \sqrt{3}}{(2 + \sqrt{3})(2 - \sqrt{3})} \] Now, apply the difference of squares to the denominator: \[ \frac{1}{x} = \frac{2 - \sqrt{3}}{4 - (\sqrt{3})^2} = \frac{2 - \sqrt{3}}{4 - 3} = \frac{2 - \sqrt{3}}{1} = 2 - \sqrt{3} \] Now, add x to \(\frac{1}{x}\): \[ x + \frac{1}{x} = (2 + \sqrt{3}) + (2 - \sqrt{3}) \] When you combine the terms, the \(\sqrt{3}\) terms will cancel out: \[ x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} = 2 + 2 = 4 \] So, \(x + \frac{1}{x}\) is equal to 4.
Solving Expression Using Distributive Property
To solve the expression given in the image, you need to apply the distributive property (also known as the FOIL method for binomials), which states that a(b + c) = ab + ac. Given the expression: (-7x - 8)(12 + 8x), we apply the distributive property as follows: (-7x * 12) + (-7x * 8x) + (-8 * 12) + (-8 * 8x) Now perform the multiplications: (-84x) + (-56x^2) - (96) - (64x) Combine like terms: -56x^2 - 84x - 64x - 96 -56x^2 - 148x - 96 The final simplified expression is: -56x^2 - 148x - 96
Solving a Mathematical Expression using Order of Operations
This mathematical expression should be solved using the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Here's how you solve the expression step-by-step: 1. Solve the expression inside the parentheses first: \(2 + 2 = 4\). 2. Then, perform the division and multiplication from left to right. The expression becomes \(8 \div 2 \times 4\). 3. Division comes first since it is to the left: \(8 \div 2 = 4\). 4. Finally, multiply the result by the number obtained from the parentheses: \(4 \times 4 = 16\). Therefore, the answer to the expression \(8 \div 2(2 + 2)\) is \(16\).
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