Example Question - foil method
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: \[ 3p(p - q) - (2p - q)^2 = -p^2 + pq - q^2 \]
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
Complex Number Multiplication
The image shows a handwritten problem which asks to compute the product of the following complex numbers: 1) \( Z_1 = 1 + 3i \) and \( Z_2 = 5 + i \) 2) \( Z_1 = 3 - 4i \) and \( Z_2 = 3 + 2i \) To compute the product of two complex numbers, you multiply them using the distributive property (also known as the FOIL method for binomials), which stands for "First, Outer, Inner, Last." Also remember that \( i^2 = -1 \). Let's solve the first product: \( Z_1 \cdot Z_2 = (1 + 3i)(5 + i) \) 1. First (1 * 5): 5 2. Outer (1 * i): i 3. Inner (3i * 5): 15i 4. Last (3i * i): 3i^2 Combining these we get: \( 5 + i + 15i + 3i^2 \) Since \( i^2 = -1 \), substitute for \( i^2 \): \( 5 + i + 15i + 3(-1) \) \( 5 + 16i - 3 \) Combine like terms: \( (5 - 3) + 16i \) \( 2 + 16i \) So the product of the first pair is \( 2 + 16i \). Now for the second product: \( Z_1 \cdot Z_2 = (3 - 4i)(3 + 2i) \) 1. First (3 * 3): 9 2. Outer (3 * 2i): 6i 3. Inner (-4i * 3): -12i 4. Last (-4i * 2i): -8i^2 Now combine these: \( 9 + 6i - 12i - 8i^2 \) Substitute \( i^2 \) with -1: \( 9 + 6i - 12i - 8(-1) \) \( 9 - 6i - 8 \) Combine like terms: \( (9 + 8) - 6i \) \( 17 - 6i \) So the product of the second pair is \( 17 - 6i \).
Expanding Algebraic Expression Using FOIL Method
The image shows an algebraic expression that needs to be expanded. To solve the expression (2x + 1)(3x + 2), we use the distributive property (also known as the FOIL method for binomials), where we multiply each term in the first parenthesis by each term in the second parenthesis. Here’s how it is expanded: (2x + 1)(3x + 2) = 2x * 3x + 2x * 2 + 1 * 3x + 1 * 2 Now, multiply the terms: = 6x^2 + 4x + 3x + 2 Combine like terms: = 6x^2 + 7x + 2 So, the expanded form of the expression is: 6x^2 + 7x + 2
Multiplication of Complex Numbers
The image shows the multiplication of two complex numbers: \( (2 - i) \) and \( (1 + i) \), where \( i \) is the imaginary unit with the property that \( i^2 = -1 \). To solve this, we apply the distributive property (FOIL method) as we would with binomials: \[ (2 - i)(1 + i) = 2(1) + 2(i) - i(1) - i(i) \] Now we simplify each term: \[ = 2 + 2i - i - i^2 \] Remember that \( i^2 = -1 \), so the expression becomes: \[ = 2 + 2i - i + 1 \] Combine like terms: \[ = (2 + 1) + (2i - i) \] \[ = 3 + i \] So, the product of \( (2 - i) \) and \( (1 + i) \) is \( 3 + i \).
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
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