product of a binomial and a trinomial Problem 1:
Multiply.
(x + 3)(x² - 5x + 7)
Problem 2:
Multiply.
(a + b)(2a² - 5ab + 3b²)
Problem 3:
Multiply.
(2x + 3y)(x² - xy + y²)
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product of a binomial and a trinomial Problem 1:
Multiply.
(x + 3)(x² - 5x + 7)
Problem 2:
Multiply.
(a + b)(2a² - 5ab + 3b²)
Problem 3:
Multiply.
(2x + 3y)(x² - xy + y²)
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Answer:
Problem 1:
To find the product of (x + 3)(x² - 5x + 7), you can use the distributive property and multiply each term of the first binomial with each term of the second trinomial:
(x + 3)(x² - 5x + 7) = x(x² - 5x + 7) + 3(x² - 5x + 7)
= x³ - 5x² + 7x + 3x² - 15x + 21
= x³ - 2x² - 8x + 21
So, the product of (x + 3)(x² - 5x + 7) is x³ - 2x² - 8x + 21.
Problem 2:
To find the product of (a + b)(2a² - 5ab + 3b²), you can again use the distributive property:
(a + b)(2a² - 5ab + 3b²) = a(2a² - 5ab + 3b²) + b(2a² - 5ab + 3b²)
= 2a³ - 5a²b + 3ab² + 2a²b - 5ab² + 3b³
= 2a³ - 3a²b - 2ab² + 3b³
Hence, the product of (a + b)(2a² - 5ab + 3b²) is 2a³ - 3a²b - 2ab² + 3b³.
Problem 3:
Similarly, to find the product of (2x + 3y)(x² - xy + y²), you can employ the distributive property:
(2x + 3y)(x² - xy + y²) = 2x(x² - xy + y²) + 3y(x² - xy + y²)
= 2x³ - 2x²y + 2xy² + 3yx² - 3xy² + 3y³
= 2x³ + yx² + 3y³
Therefore, the product of (2x + 3y)(x² - xy + y²) is 2x³ + yx² + 3y³.
Answer:
Problem 1:
To multiply (x + 3)(x² - 5x + 7), we'll use the distributive property. Multiply each term of the first parentheses with each term of the second parentheses and combine like terms if necessary.
(x + 3)(x² - 5x + 7)
= x(x² - 5x + 7) + 3(x² - 5x + 7)
Now, distribute each term:
= x³ - 5x² + 7x + 3x² - 15x + 21
Combine like terms:
= x³ - 2x² - 8x + 21
The product of (x + 3)(x² - 5x + 7) is x³ - 2x² - 8x + 21.
Problem 2:
To multiply (a + b)(2a² - 5ab + 3b²), again, we'll use the distributive property. Multiply each term of the first parentheses with each term of the second parentheses and combine like terms if necessary.
(a + b)(2a² - 5ab + 3b²)
= a(2a² - 5ab + 3b²) + b(2a² - 5ab + 3b²)
Now, distribute each term:
= 2a³ - 5a²b + 3ab² + 2a³ - 5ab² + 3b³
Combine like terms:
= 4a³ - 5a²b - 5ab² + 3b³
The product of (a + b)(2a² - 5ab + 3b²) is 4a³ - 5a²b - 5ab² + 3b³.
Problem 3:
To multiply (2x + 3y)(x² - xy + y²), we'll once again apply the distributive property. Multiply each term of the first parentheses with each term of the second parentheses and combine like terms if needed.
(2x + 3y)(x² - xy + y²)
= 2x(x² - xy + y²) + 3y(x² - xy + y²)
Now, distribute each term:
= 2x³ - 2x²y + 2xy² + 3yx² - 3xy² + 3y³
Combine like terms:
= 2x³ + (3y)x² + (-2xy + 2xy) + (2xy² - 3xy²) + 3y³
Simplify further:
= 2x³ + 3yx² + 3y³
The product of (2x + 3y)(x² - xy + y²) is 2x³ + 3yx² + 3y³.