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Chapter 5: Problem 100

Perform the indicated operations. $$(y+5)^{2}-(y-4)^{2}$$

Short Answer

Expert verified
The result after performing the indicated operations is \(18y + 9\)

Step by step solution

01

Expand the Squares

Expand the squares in the given expression using the formula \((a+b)^{2}= a^{2} + 2ab + b^{2}\) and \((a-b)^{2}= a^{2} - 2ab + b^{2}\) . Hence, \((y+5)^{2} = y^{2} + 10y + 25\) and \((y-4)^{2} = y^{2} - 8y + 16\)
02

Subtract the Squares

Using the formula for the difference of squares: \(a^{2} - b^{2} = (a+b)(a-b)\) , where a is \((y + 5)^{2}\) and b is \((y - 4)^{2}\). So, \((y+5)^{2} - (y-4)^{2} = ((y^{2} + 10y + 25) - (y^{2} - 8y + 16))\)
03

Simplify the Expression

Simplify the obtained expression by collecting like terms: \(y^{2} + 10y + 25 - y^{2} + 8y - 16 = 18y + 9\)

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Most popular questions from this chapter

Explain how to divide a polynomial that is not a monomial by a monomial. Give an example.

Perform the indicated operations. $$4 x^{2}\left(5 x^{3}+3 x-2\right)-5 x^{3}\left(x^{2}-6\right)$$

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