The factorization of the expression 36x⁴y³ - 16x³y is 4x³y(9xy² - 4)
<h3>Factorization</h3>
Factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorization of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.
To the factor, a number means to break it up into numbers that can be multiplied to get the original number.
In the given expression, 36x⁴y³ - 16x³y can be factorized as
36x⁴y³ - 16x³y = 4x³y(9xy² - 4)
The common factor in the expression is 4x³y
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Answer:
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Step-by-step explanation:
Your answer is: $3.15 each.
Here are the steps:
First, I added $2.82 and $1.43. Then, I subtracted the sum ($4.25) from $20. Lastly, I divided the difference($15.75) by five because there were five pineapples. Which gave me the answer: $3.15.
Explanation:
It helps to understand the process of multiplying the binomials. Consider the simple case ...
(x +a)(x +b)
The product is ...
(x +a)(x +b) = x² +(a+b)x + ab
If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.
If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).
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Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.
<u>Example</u>:
x² -x -6
-6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.
-6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)
The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.
x² -x -6 = (x -3)(x +2)
