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Chapter 5: Problem 99

Perform the indicated operations. $$(y+6)^{2}-(y-2)^{2}$$

Short Answer

Expert verified
The result of the operation \((y+6)^{2}-(y-2)^{2}\) is \(16y + 32\).

Step by step solution

01

Write out the formula

First, we know the formulas for the difference of squares and the square of a binomial. The difference of squares formula is \(a^{2} - b^{2} = (a + b)(a - b)\), and the square of a binomial formula is \((a + b)^2 = a^2 + 2ab + b^2\).
02

Apply the square of a binomial formula

Apply the square of a binomial formula to \((y+6)^{2}\) and \((y-2)^{2}\). This gives us \(y^{2} + 2*6*y + 6^{2}\) and \(y^{2} - 2*2*y + 2^{2}\), which simplify to \(y^2 + 12y + 36\) and \(y^2 - 4y + 4\).
03

Subtract the two results

Finally, subtract \((y^2 - 4y + 4)\) from \((y^2 + 12y + 36)\) to get our result. This gives us \((y^2 + 12y + 36) - (y^2 - 4y + 4)\), which simplifies to \(16y + 32\).

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Most popular questions from this chapter

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

Find each of the products in parts (a)-(c). a. \((x-1)(x+1)\) b. \((x-1)\left(x^{2}+x+1\right)\) c. \((x-1)\left(x^{3}+x^{2}+x+1\right)\) d. Using the pattern found in parts (a)-(c), find $(x-1)\left(x^{4}+x^{3}+x^{2}+x+1\right) without actually multiplying.

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