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Chapter 0: Problem 64

Find each product. $$\left(7 x^{2} y+1\right)\left(2 x^{2} y-3\right)$$

Short Answer

Expert verified
The product of \(7 x^{2} y+1\) and \(2 x^{2} y-3\) is \(14x^{4}y^{2} - 21x^{2}y + 2x^{2}y - 3\)

Step by step solution

01

Distribute the first term of the first expression

Multiply the first term of the first expression (\(7x^{2}y\)) by each term in the second expression, which gives: \(7x^{2}y \cdot 2x^{2}y - 7x^{2}y \cdot 3\). This simplifies to: \(14x^{4}y^{2} - 21x^{2}y\)
02

Distribute the second term of the first expression

Multiply the second term of the first expression (1) by each term in the second expression, which gives: \(1 \cdot 2x^{2}y - 1 \cdot 3\). This simplifies to: \(2x^{2}y - 3\)
03

Combine all the terms

Combine all the terms from steps 1 and 2 to get the final product: \(14x^{4}y^{2} - 21x^{2}y + 2x^{2}y - 3\)

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