Example Question - combine like terms
Here are examples of questions we've helped users solve.
Simplifying Expressions Using the Distributive Property
1. Apply the distributive property to 3p(p - q): 3p * p - 3p * q = 3p^2 - 3pq 2. Expand the square of the binomial (2p - q)^2: (2p - q)(2p - q) = 4p^2 - 4pq + q^2 3. Subtract the expanded binomial from the first expression: (3p^2 - 3pq) - (4p^2 - 4pq + q^2) 4. Distribute the negative sign to each term in the second expression: 3p^2 - 3pq - 4p^2 + 4pq - q^2 5. Combine like terms: -p^2 + pq - q^2 So the simplified expression is: -p^2 + pq - q^2
Solving an Algebraic Expression by Combining Like Terms
To solve the expression given in the image, you simply need to combine the like terms. Like terms are terms that have the same variables raised to the same power. Here, both terms are like terms since they both have 'b' as the variable. You simply add the coefficients (the numerical parts) of these like terms: 13b + 27b = (13 + 27)b = 40b So, the expression simplifies to 40b.
Simplifying Square Roots by Factoring Out Perfect Squares and Combining Like Terms
To solve the expression given in the image, you need to simplify the square roots by factoring out perfect squares and then combine like terms. The expression is: \( 5\sqrt{20} - 12\sqrt{45} \) First, let's simplify \( \sqrt{20} \) and \( \sqrt{45} \). For \( \sqrt{20} \), we look for the largest perfect square that is a factor of 20, which is 4. So we can write 20 as \( 4 \times 5 \), then take the square root of each factor: \( \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2 \sqrt{5} \) Now for \( \sqrt{45} \), the largest perfect square factor is 9. So we can write 45 as \( 9 \times 5 \), then take the square root of each factor: \( \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3 \sqrt{5} \) Now, we replace the square roots in the original expression with their simplified forms: \( 5\cdot2\sqrt{5} - 12\cdot3\sqrt{5} \) This simplifies to: \( 10\sqrt{5} - 36\sqrt{5} \) Now we can combine like terms: \( (10 - 36)\sqrt{5} \) \( -26\sqrt{5} \) So, the simplified form of the original expression is: \( -26\sqrt{5} \)
Algebraic Expression Simplification Guide
The image shows an algebraic expression that needs to be simplified. The expression is: \[ \frac{5}{6}(2ab - ab^2) - (-a^2b) - (3a^2 + \frac{3}{2}ab^2) + \frac{3}{4}a^2b^2 \] Unfortunately, the visibility of the full expression is limited by the resolution of the image. However, based on what is visible, here is what you can do to simplify the expression: 1. Distribute the fractions within the parentheses across the terms they are multiplying. 2. Combine like terms, which are terms that have the same variables to the same power. 3. Simplify the expression by adding or subtracting the coefficients of the like terms. Given the visible portion of the problem, let's demonstrate the first step with the first two terms: \[ \frac{5}{6} \times 2ab = \frac{5 \times 2}{6} ab = \frac{10}{6} ab = \frac{5}{3} ab \] \[ \frac{5}{6} \times (-ab^2) = \frac{5 \times (-1)}{6} ab^2 = \frac{-5}{6} ab^2 \] However, without the full expression, I cannot provide a complete answer. If you can provide the entire problem with higher image quality or text form, I would be able to continue with the simplification.
Solving a Linear Equation with Fractions
To solve the equation in the image, follow these steps: \( \frac{3}{2} - (2x - 8) = 5 - 2(5x - 7) - 5 \) First, distribute the negative sign through the parentheses on the left side: \( \frac{3}{2} - 2x + 8 = 5 - 2(5x - 7) - 5 \) Next, distribute the -2 on the right side: \( \frac{3}{2} - 2x + 8 = 5 - 10x + 14 - 5 \) Combine like terms on the right side: \( \frac{3}{2} - 2x + 8 = 14 - 10x \) Now, to get rid of the fraction on the left side, multiply every term in the equation by 2: \( 2 * \frac{3}{2} - 2 * 2x + 2 * 8 = 2 * 14 - 2 * 10x \) Simplify: \( 3 - 4x + 16 = 28 - 20x \) Now combine like terms on the left side: \( 19 - 4x = 28 - 20x \) Next, we want to get all the x terms on one side and constants on the other. Add 20x to both sides: \( 19 - 4x + 20x = 28 - 20x + 20x \) Simplify: \( 19 + 16x = 28 \) Subtract 19 from both sides to isolate the term with x: \( 19 + 16x - 19 = 28 - 19 \) Simplify: \( 16x = 9 \) Finally, divide by 16 to solve for x: \( x = \frac{9}{16} \) So the solution to the equation is \( x = \frac{9}{16} \).
Expanding and Simplifying Algebraic Expression
To expand the brackets and simplify the expression \(2(3x - 7) + 19\), we will first distribute the 2 through the terms inside the parenthesis and then combine like terms. Here are the steps: 1. Distribute the 2 to both terms inside the brackets: \(2 \times 3x\) and \(2 \times -7\). \(2(3x) = 6x\) \(2(-7) = -14\) 2. Combine these results with the remaining term outside the brackets: \(6x - 14 + 19\) 3. Simplify the constant terms \(-14\) and \(+19\) by adding them together: \(-14 + 19 = 5\) Put it all together, and the simplified expression is: \(6x + 5\)
Simplifying Algebraic Expression with Exponents
To simplify the expression given, we'll apply the rules of exponents and combine like terms. The expression is: \[ \frac{10x^{5n+4} + 125x^{5n+2}}{3x^{5n+3} - 20x^{5n+1}} \] Starting with the numerator: \[ 10x^{5n+4} + 125x^{5n+2} \] This expression cannot be simplified further because the terms are not like terms (they have different exponents). Now let's look at the denominator: \[ 3x^{5n+3} - 20x^{5n+1} \] Similarly, this expression cannot be simplified further because the terms are not like terms (they have different exponents). Since we cannot simplify the individual parts of the numerator or the denominator any further, we can only simplify if there's a common factor in both the numerator and the denominator. Given that the exponents in each term of the numerator are different from those in the denominator, there are no obvious factors that would cancel out. Therefore, the expression is already in its simplest form: \[ \frac{10x^{5n+4} + 125x^{5n+2}}{3x^{5n+3} - 20x^{5n+1}} \]
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