In Exercises 67–82, find each product. (7x2 y+1)(2x2 y−3)

Ch. P - Fundamental Concepts of Algebra

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problema 72

Capitolo 1, Problema 72

In Exercises 67–82, find each product. (7x² y+1)(2x² y−3)

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Distribute each term in the first polynomial $(7x^2y + 1)$ to each term in the second polynomial $(2x^2y - 3)$. This is done using the distributive property $(a + b)(c + d) = ac + ad + bc + bd$.

Multiply the first term $7x^2y$ in the first polynomial by the first term $2x^2y$ in the second polynomial. This gives $7x^2y \cdot 2x^2y = 14x^4y^2$.

Multiply the first term $7x^2y$ in the first polynomial by the second term $-3$ in the second polynomial. This gives $7x^2y \cdot -3 = -21x^2y$.

Multiply the second term $1$ in the first polynomial by the first term $2x^2y$ in the second polynomial. This gives $1 \cdot 2x^2y = 2x^2y$.

Multiply the second term $1$ in the first polynomial by the second term $-3$ in the second polynomial. This gives $1 \cdot -3 = -3$. Combine all the terms from the previous steps to form the expanded polynomial.

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Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial. This process is often referred to as the distributive property, where you multiply coefficients and add the exponents of like bases. Understanding this concept is crucial for correctly expanding the product of polynomials.

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