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This is one of our many quizzes on Polynomial special products. Click on this to access more such competitive quizzes on Algebra.

Polynomial special products Quiz 2

mathematics

 Identify the special product from the following –

 Test if each of the options satisfy the condition of being a special product. Eliminating the incorrect options, we can find the correct answer.

In option $(b)$ and $(d)$ the constant terms have a negative sign with them so they are not special products. $ \\ $ In option $(a)$ there is no constant term so it is not a special product. $ \\ $ From option $(c)$ $ \\ 25{x^2} - 90x + 81$ as ${(5x)^2} - 2 \times 5x \times 9 + {(9)^2} \\ 25{x^2} - 90x + 81 = {(5x - 9)^2}$

 What is the simplified form of $(x + 9y + 11)(x + 9y + 11)$

 Use the formula for finding the square of a trinomial to find the correct answer.

$  {(a + b + c)^2} = {a^2} + {b^2} + {c^2} + 2ab + 2bc + 2ca   \\  (x + 9y + 11)(x + 9y + 11) = {(x + 9y + 11)^2}   \\   \Rightarrow (x + 9y + 11)(x + 9y + 11) = {x^2} + 81{y^2} + 121 + 18xy + 198y + 22x   \\  $

 Find the product of these two numbers without using calculator – $22 \times 38$

 To find the product of two big numbers, try to express them as a sum and difference of two same numbers,

$22 = 30 - 8$ and $38 = 30 + 8$ , $ \\ $ So $22 \times 38 = (30 - 8)(30 + 8)$ $ \\ $ We know $(a - b)(a + b) = {a^2} - {b^2}$ $ \\ 22 \times 38 = {(30)^2} - {(8)^2}   \\   \Rightarrow 22 \times 38 = 900 - 64   \\   \Rightarrow 22 \times 38 = 836   \\  $

 Find the square of 31 without using a calculator.

 To find the square of a large number, try to express it as the sum or difference of two small numbers whose squares can be calculated easily.

$  31 = 30 + 1   \\   \Rightarrow {(31)^2} = {(30 + 1)^2}   \\  $ We know ${(a + b)^2} = {a^2} + 2ab + {b^2}$ $ \\ {(31)^2} = {(30)^2} + 2 \times 30 \times 1 + {(1)^2}   \\   \Rightarrow {(31)^2} = 900 + 60 + 1   \\   \Rightarrow {(31)^2} = 961   \\  $

 Each wall of a house has an area equal to the product of the base and the height of the wall. If the base and height of all the walls are equal and are increased by 3 units, then the total increase in the area of walls is equal to?

 Total increase in area of walls is equal to the difference of the final total area of walls and initial total area of walls

When the length of base and height of each height is equal to $x$ , area of each wall is ${x^2}$. $ \\ $ All the houses have 4 walls, so total area of walls is $4{x^2}$ $ \\ $ Now, the length of the base and height of all the walls is increased by 3 units, so new length is $x + 3$ $ \\ $ New area of wall is $(x + 3)(x + 3) = {(x + 3)^2}$ $ \\ $ We know ${(a + b)^2} = {a^2} + {b^2} + 2ab$ $ \\ $ So ${(x + 3)^2} = {x^2} + 6x + 9$ $ \\ $ Total area of walls is $4({x^2} + 6x + 9) = 4{x^2} + 24x + 36$ $ \\ $ Total increase in area of walls $ = [4{x^2} + 24x + 36] - [4{x^2}] = 24x + 36$