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Example Question - simplify algebraic expressions

Here are examples of questions we've helped users solve.

Solving the Expression with Distribution and Expansion

To solve the expression given in the image: 1. Distribute the \( 3p \) across \( (p - q) \): \[ 3p \cdot p + 3p \cdot (-q) \] 2. Expand the square \( (2p - q)^2 \) using the FOIL (First, Outer, Inner, Last) method: \[ (2p - q)(2p - q) \] \[ 2p \cdot 2p + 2p \cdot (-q) + (-q) \cdot 2p + (-q) \cdot (-q) \] Combine the above expansions: \[ 3p^2 - 3pq - (4p^2 - 2pq - 2pq + q^2) \] 3. Expand the negative sign into the second parenthesis: \[ 3p^2 - 3pq - 4p^2 + 2pq + 2pq - q^2 \] 4. Combine like terms: \[ 3p^2 - 4p^2 - 3pq + 2pq + 2pq - q^2 \] \[ -p^2 + pq - q^2 \] Therefore: \[ 3p(p - q) - (2p - q)^2 = -p^2 + pq - q^2 \]

Solving Expression Involving Variables

Die Gleichung auf dem Bild lautet: 13.6x √(a² + b²) + 4/8 = ? Um den Ausdruck zu vereinfachen, könnten wir zuerst den Term 4/8 vereinfachen. Dieser ergibt 0.5, da 4 durch 8 geteilt eine halbe ergibt. Nun sieht die Gleichung so aus: 13.6x √(a² + b²) + 0.5 = ? Diese Gleichung kann nicht weiter gelöst werden, ohne spezifische Werte für die Variablen a, b und x zu haben. Wenn du Werte für a, b und x hast, können wir den Ausdruck berechnen.

Simplifying a Mathematical Expression

Claro, vamos a simplificar la expresión matemática escrita en la imagen. La expresión es: \[ 2 \left( \frac{x^{5} + 3\sqrt{x} - 1}{x^4} \right) \] Para simplificar esta expresión, podemos dividir cada término dentro de los paréntesis por \( x^4 \) y luego multiplicar por 2: \[ 2 \left( \frac{x^{5}}{x^4} + \frac{3\sqrt{x}}{x^4} - \frac{1}{x^4} \right) \] Ahora simplificamos cada término: \[ 2 \left( x^{5-4} + 3x^{\frac{1}{2}-4} - x^{-4} \right) \] \[ 2 \left( x + 3x^{-\frac{7}{2}} - x^{-4} \right) \] Multiplicamos cada término por 2: \[ 2x + 2 \cdot 3x^{-\frac{7}{2}} - 2x^{-4} \] \[ 2x + 6x^{-\frac{7}{2}} - 2x^{-4} \] Esto nos da la expresión simplificada.

Simplifying Algebraic Expressions with Exponents

The given expression is: \((8a^4x^2y^2)^2 \div a^6x^2y^{-1}\) To solve it, we will first apply the power to the terms inside the parentheses and then divide by the terms outside the parentheses. Applying the power of 2 to each term inside the parentheses: \(= (8^2 \cdot (a^4)^2 \cdot (x^2)^2 \cdot (y^2)^2)\) Calculating each term separately: \(8^2 = 64\) \((a^4)^2 = a^{4 \cdot 2} = a^8\) \((x^2)^2 = x^{2 \cdot 2} = x^4\) \((y^2)^2 = y^{2 \cdot 2} = y^4\) So after applying the power we have: \(= 64a^8x^4y^4\) Now we will divide this by \(a^6x^2y^{-1}\): \(= \frac{64a^8x^4y^4}{a^6x^2y^{-1}}\) Dividing each term: \(64\) is just a constant, so it stays as is. For \(a\), we subtract exponents (when dividing with the same base, subtract the exponents): \(a^{8-6} = a^2\). For \(x\), similarly: \(x^{4-2} = x^2\). For \(y\), we add the exponents because one of them is negative: \(y^{4-(-1)} = y^{4+1} = y^5\). So the simplified expression is: \(= 64a^2x^2y^5\) This is the final answer.

Simplifying Algebraic Expression by Division

To solve the given expression, you need to simplify it by dividing both the numerical coefficients and the variables with exponents. Given expression: \( \frac{10x^8}{5x^4} \) First, divide the coefficients (numbers in front of the variables): \( \frac{10}{5} = 2 \) Next, use the quotient rule of exponents for \( x^8 \div x^4 \) which states that when you divide two expressions that have the same base, you subtract the exponents: \( x^{8-4} = x^4 \) So the simplified expression is: \( 2x^4 \)

Algebraic Expression Simplification

The image shows an algebraic expression that requires simplification: (2√x - √y)(6√x + 5√y) This is a binomial multiplication problem, which we can solve using the FOIL method, where FOIL stands for "First, Outer, Inner, Last." This means we multiply the first terms in each binomial, then the outer terms, followed by the inner terms, and finally the last terms, combining like terms where possible. Here's how we apply FOIL to this problem: First: (2√x)*(6√x) = 12x Outer: (2√x)*(5√y) = 10√xy Inner: (-√y)*(6√x) = -6√xy Last: (-√y)*(5√y) = -5y Combining these results, we get: 12x + 10√xy - 6√xy - 5y Combine like terms: 12x + (10√xy - 6√xy) - 5y 12x + 4√xy - 5y The simplified form of the expression is: 12x + 4√xy - 5y

Simplifying Algebraic Expression with Exponents

The expression in the image is \[ x^2 \cdot (x^2 + 1)^{-1/2} - (x^2 + 1)^{1/2} \div x^2 \] First, we'll simplify the term in the denominator of the first fraction by moving it to the numerator with a negative exponent: \[ x^2 \cdot (x^2 + 1)^{-1/2} - (x^2 + 1)^{1/2} \cdot x^{-2} \] Now, we'll combine the terms by finding a common exponent for \( x \). In this case, we want to match the exponent of \( x \) to the smallest exponent, which is \( -2 \): \[ x^{2-2} \cdot (x^2 + 1)^{-1/2} - (x^2 + 1)^{1/2} \cdot x^{-2} \] Upon simplifying \( x^{2-2} \), we get: \[ (x^2 + 1)^{-1/2} - (x^2 + 1)^{1/2} \cdot x^{-2} \] The expression cannot be simplified further because the terms are not like terms (they have different exponents). Therefore, the simplified expression is: \[ (x^2 + 1)^{-1/2} - (x^2 + 1)^{1/2} \cdot x^{-2} \]

Simplifying Algebraic Expressions with Exponents

Sure, to simplify the expression provided in the image, we need to follow the rules of algebra and exponents. The expression in the image is: (10 × 5^n^4 + 125 × 5^n^2) / (3 × 5^n^3 + 20 × 5^n^1) Let's simplify the numerator and the denominator separately. First, we can factor out the greatest common factor in the numerator, which is 5^n^2: = 5^n^2 (10 × 5^n^2 + 125) / (3 × 5^n^3 + 20 × 5^n^1) And then we can do the same for the denominator, where the greatest common factor is 5^n^1: = 5^n^2 (10 × 5^n^2 + 125) / 5^n^1 (3 × 5^n^2 + 20) Now, let's simplify the terms inside the parentheses: Numerator: 10 × 5^n^2 + 125 can be simplified to 5^n^2 + 125. Since no further simplification can be done inside the parentheses (assuming the "+ 125" is not supposed to have a power of 5 associated with it), let's keep it as is. Denominator: 3 × 5^n^2 + 20 simplifies to 3 × 5^n^2 + 20. Again, assuming "20" does not have a power of 5 associated with it, there's no further simplification inside the parentheses. So now we have: = 5^n^2 (5^n^2 + 125) / 5^n^1 (3 × 5^n^2 + 20) Now, let's simplify across the numerator and denominator by canceling common factors where possible. We can cancel one 5^n^1 from both the numerator and the denominator: = 5^n (5^n^2 + 125) / (3 × 5^n^2 + 20) We cannot simplify further without knowing the value of n. If n is such that n^2, n^1, and the simple numerical terms 125 and 20 can be simplified further, we'd do that. Otherwise, this is the simplified form of the given expression. Please note that the superscripts in the original expression might be ambiguous due to the resolution and angle of the photo. If the powers are not correctly interpreted, please provide more information or adjust the expression accordingly.

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: \[ \frac{10x^{5n+4} + 125x^{5n+2}}{3x^{5n+3} - 20x^{5n+1}} \]