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Answer:

Question 4. (x-5)² and (4c-3)(4c+3)

Question 5. Expressions for the areas are 8(7x-1)(x-2) and -8(7x-1)(x-2).

Question 6. Buyer is not right as the values of x are not same.

Step-by-step explanation:

Question 4). x²- 10x+25 = x²-2×5x+5²

                                       = (x-5)² since (a-b)² = a²+b²-2ab

                            16c²-9 = (4c)²- 3²

                                      = (4c-3)(4c+3)  Since a²-b²=(a-b)(a+b)

Question 5). Area of one square painting = 81x²-90x+25 =(9x-5)²

               Area of second square painting = 25x²+30x+9 =(5x+3)²

Now the difference between the areas of these two paintings

= 81x²-90x+25-(25x²+30x+9) = (9x-5)²-(5x+3)²

= (9x-5+5x+3)(9x-5-5x-3) = (14x-2)(4x-8) = 8(7x-1)(x-2)

Since we have to calculate the difference of the areas of two paintings then it may also be written as 25x²+30x+9-(81x²-90x+25)= -8(7x-1)(x-2)

Question.6 The areas are given as 1600 in² and 484 in² then

(9x-5)²= 1600 ⇒ (9x-5) =√1600

9x-5 =40 ⇒ 9x = 40+5 =45

Or x=45/9 =5

and for other painting (5x+3)²=484

                                    5x+3=√484 = 22

                                    5x =22-3

                                    5x =19 ⇒ x=19/5

So the values of x are not same. So buyer is not right.


                   

                 



smmwaite

Answer:

4 part 1:  Error was in the second step (2(x)(5)

 part 2: Error was in the second step (4c)² - 3³ ≠ (4c - 3)²


5.  part 1:     56x² + 60x + 16

    part 2: The values of x in the 2 expressions are not the same.


Step-by-step explanation:

Question 4 part 1

x² - 10x + 25

the factors are -5 and -5

x² - 5x - 5x + 25 = x(x-5) - 5(x-5)

foctoring out (x-5)

   = (x-5)(x-5) = (x - 5)²

Question 4 part 2

16c² - 9 = (4c)² - 3²

This is a different of 2 squares

(4c)² - 3² = (4c - 3)(4c + 3)


question 5

part 1

Subtracting the two quadratic expressions

  81x² + 90x + 25 - (25x² + 30x + 9)

  =    81x² + 90x + 25 - 25x² - 30x - 9

 = 56x² + 60x + 16

part 2 solving for x

81x² + 90x + 25 = 1600

81x² + 90x = 1600-25

9x² + 10x = 175

x² + 1.111x + 0.556² = 175 + 0.3086

(x + 0.556)² = 175.3086

x = ±13.2404 - 0.556

   = 12.6844 or -13.7964


25x² + 30x + 9 = 484

25x² + 30x = 484 - 9

x² + 1.2x + 0.6² = 19+0.36

(x + 0.6)² = 19.36

x = ±4.4 - 0.6

   = 3.8   or  -5


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