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Chapter 5: Problem 70

Find each product. In each case, neither factor is a monomial. $$(y-2)\left(y^{2}-4 y+3\right)$$

Short Answer

Expert verified
The product of \((y-2)\) and \((y^2-4y+3)\) is \(y^3-6y^2+11y-6\).

Step by step solution

01

Distribute the Terms in the First Polynomial to Each Term in the Second Polynomial

Start by applying the distributive property of multiplication over addition. This means multiply every term in the first polynomial by every term in the second polynomial. Doing this will give: \(y*(y^2)-y*(4y)+y*3-2*y^2+2*4y-2*3\).
02

Simplify Each Resulting Term

Next, carry out each multiplication. This will result in the following terms: \(y^3-4y^2+3y-2y^2+8y-6\).
03

Combine Like Terms

Now the final step is to combine like terms, which means add or subtract the coefficients of the terms that have the same variable raised to the same power. This results in \(y^3-6y^2+11y-6\).

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Most popular questions from this chapter

Perform the indicated computations. Express answers in scientific notation. $$\left(2 \times 10^{2}\right)\left(2.6 \times 10^{-3}\right) \div\left(4 \times 10^{3}\right)$$

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