The product of two polynomial is (b - c)(a - d)
Step-by-step explanation:
Let us explain the meaning of polynomial
A polynomial is an expression consisting of:
- Coefficients
- Involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables
∵ a(b - c) + d(c - b)
∵ We need to write it as a product of two polynomials
- That means factorize it to have two brackets multiplied by
each other and each one has 2 terms
∵ The bracket (c - b) can be written as (-b + c)
- Take (-1) as a common factor from the bracket (-b + c)
∵ -b ÷ (-1) = b
∵ c ÷ (-1) = -c
∴ (-b + c) = - (b - c)
- Substitute it in the expression above
∴ a(b - c) + d(c - b) = a(b - c) + d(-1)(b - c)
∵ d(-1) = -d
∴ a(b - c) + d(c - b) = a(b - c) - d(b - c)
Let us factorize the expression a(b - c) - d(b - c)
The bracket (b - c) is a common factor of the two terms
∵ (b - c) is a common factor of the two terms of the expression
∵ a(b - c) ÷ (b - c) = a
∵ - d(b - c) ÷ (b - c) = - d
∴ a(b - c) - d(b - c) = (b - c)(a - d) ⇒ product of 2 polynomial
The product of two polynomial is (b - c)(a - d)
Learn more:
You can learn more about factorization in brainly.com/question/7932185
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