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This is the second of our many quizzes on multiplying polynomials. Click on this to access more such competitive quizzes on polynomials.

Multiplying Polynomials Quiz 2

mathematics

 Multiply each term of the first polynomial to the second polynomial.

 $\text{Given: }(2{{x}^{2}}-1)(4x+5) \\ \Rightarrow 2{{x}^{2}}(4x+5)-1(4x+5) \\ \Rightarrow 8 {{x}^{3}}+10{{x}^{2}}-4x-5 $

 Multiply: $(9y+5z)({{y}^{2}}-3yz+{{z}^{2}})$ 

 Multiply each term of the first polynomial to second polynomial.

 $\text{Given: }(9y+5z)({{y}^{2}}-3yz+{{z}^{2}})\\ \Rightarrow 9y({{y}^{2}}-3yz+{{z}^{2}})+5z({{y}^{2}}-3yz+{{z}^{2}}) \\ \Rightarrow 9{{y}^{3}}-22{{y}^{2}}z-6y{{z}^{2}}+5{{z}^{3}} $ 

 Firstly, we will expand ${{(x-7)}^{2}}$ using the formula ${{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}$ and then multiply each term of the first polynomial to each term of the second polynomial.

 $\text{Given: }{{(x-7)}^{2}}(4x-1)\\ \Rightarrow (4x-1)({{x}^{2}}-14x+49) \\ \Rightarrow 4x({{x}^{2}}-14x+49)-1({{x}^{2}}-14x+49) \\ \Rightarrow 4{{x}^{3}}-57{{x}^{2}}+210x-49 $

 Multiply: $(2x+5y)(4x-10y)({{x}^{2}}-2y)({{x}^{2}}+2y)$ 

 First we will take 2 common from the second polynomial and then we will use the formula ${{a}^{2}}-{{b}^{2}}=(a+b)(a-b)$ to find out the solution.

 $\text{Given equation can also be written as,}\\ (2x+5y)(2)(2x-5y)({{x}^{2}}-2y)({{x}^{2}}+2y) \\ \text{Using the formula, }{{a}^{2}}-{{b}^{2}}=(a+b)(a-b), \\ \Rightarrow 2({{(2x)}^{2}}-{{(5y)}^{2}})({{({{x}^{2}})}^{2}}-{{(2y)}^{2}}) \\ \Rightarrow 8{{x}^{6}}-32{{x}^{2}}{{y}^{2}}-50{{x}^{4}}{{y}^{2}}+200{{y}^{4}} $

 If the cost of fencing is Rs. 10/m, then what will be the mathematical expression for cost of fencing a rectangular garden whose length is $5x – 1$ m and the width is $3$ m less than its length?

 From the given condition, we will find the width and then find the perimeter using the formula to get the required answer.

 <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/aa4e1610-5def-4f07-9362-a11b086098666896282905010505693.png"/>$\\ \text{Length of the garden }= 5x – 1m. \\ \text{ Then, the width of the garden }= 5x – 1 – 3 = (5x - 4)m. \\ \text{Perimeter of the rectangular garden }= 2\text{(length + width)m} \\ \Rightarrow 2(5x-1+5x-4)\text{m} \\ \Rightarrow 20x-10\text{m} \\\therefore \text{Required cost} = 10\text{(Perimeter)} \\ \Rightarrow 10(20x-10) \\ \Rightarrow 200x-100 $