The product of the two binomials is (y + 1)(y - 5)
Step-by-step explanation:
To write a polynomial as a product of two binomials
∵ The polynomial is (y - 5) - y(5 - y)
- Multiply y by the bracket (5 - y)
∵ y(5 - y) = y(5) - y(y)
∴ y(5 - y) = 5y - y²
- Substitute 5(5 - y) by (5y - y²)
∴ (y - 5) - y(5 - y) = (y - 5) - (5y - y²)
- Multiply (-) by the bracket (5y - y²)
∵ (-)(5y) = -5y
∵ (-)(-y²) = y²
∴ (y - 5) - y(5 - y) = y - 5 - 5y + y²
- Add the like terms
∴ (y - 5) - y(5 - y) = -4y - 5 + y²
- Arrange the terms from greatest power of y
∴ (y - 5) - y(5 - y) = y² - 4y - 5
Now let us factorize y² - 4y - 5 into two factors
∵ y² = y × y
∵ -5 = -5 × 1
- Multiply y by 1 and y by -5, then add the product the sum
must be equal the middle term of the polynomial above
∵ y(1) + y(-5) = y - 5y = -4y ⇒ as the middle term
- Now write the two bracts
∴ y² - 4y - 5 = (y + 1)(y - 5)
The product of the two binomials is (y + 1)(y - 5)
Learn more:
You can learn more about the polynomials in brainly.com/question/12700460
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