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26.06.2022

Factor this expression completely. x2 - r2

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30.05.2023, solved by verified expert

Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee

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This can be factored as a difference of two squares. When you have a difference of two squares (a² - b²), it will factor out into (a + b) (a - b).

(x² - r²)
(x + r)(x - r)

You can multiply the two groups to double check it.

(x + r)(x - r)
x² - rx + rx - r²
x² - r²

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Mathematics

Factor this expression completely. x2 - r2

Step-by-step answer

P Answered by Master

4

This can be factored as a difference of two squares. When you have a difference of two squares (a² - b²), it will factor out into (a + b) (a - b).

(x² - r²)
(x + r)(x - r)

You can multiply the two groups to double check it.

(x + r)(x - r)
x² - rx + rx - r²
x² - r²

Mathematics

Factor the expression completely. 8x2 - 18

Step-by-step answer

P Answered by PhD

6

2 ( 2x-3) (2x+3)

Step-by-step explanation:

8x^2 - 18

Factor out a 2

2(4x^2 -9)

Inside the parentheses is the difference of squares

2 ((2x)^2 - 3^2)

We know the difference of squares is (a^2 -b^2) = (a-b)(a+b)

2 ( 2x-3) (2x+3)

Mathematics

Factor the expression completely. 8x2 - 18

Step-by-step answer

P Answered by PhD

6

2 ( 2x-3) (2x+3)

Step-by-step explanation:

8x^2 - 18

Factor out a 2

2(4x^2 -9)

Inside the parentheses is the difference of squares

2 ((2x)^2 - 3^2)

We know the difference of squares is (a^2 -b^2) = (a-b)(a+b)

2 ( 2x-3) (2x+3)

Mathematics

Factor the expression completely. 4x2 - 12x + 9

Step-by-step answer

P Answered by PhD

2

(2x - 3)(2x - 3)
the answer to the question

Mathematics

Factor the expression completely. 64x2 - 4

Step-by-step answer

P Answered by Master

2

4(16x^2 - 1)

Step-by-step explanation:

You mean 64x^2 - 4 ? If so, we can take out a factor of to get 4(16x^2 - 1)

Mathematics

Factor the expression completely. 4x2 - 12x + 9

Step-by-step answer

P Answered by PhD

2

(2x - 3)(2x - 3)
the answer to the question

Mathematics

Factor the expression completely. 64x2 - 4

Step-by-step answer

P Answered by Master

2

4(16x^2 - 1)

Step-by-step explanation:

You mean 64x^2 - 4 ? If so, we can take out a factor of to get 4(16x^2 - 1)

Mathematics

Factor the expression completely. 18x2 - 8

Step-by-step answer

P Answered by PhD

1

28

Step-by-step explanation:

You must multiply first using BODMAS oe BIDMAS, then add on.

18x2= 36

36-8= 28

Mathematics

Factor the expression completely. 7x - x2

Step-by-step answer

P Answered by PhD

2

x(7 - x)

Step-by-step explanation:

Given

7x - x² ← factor out x from both terms

= x(7 - x) ← in factored form

Mathematics

1) Which is a binomial factor of 8x2 + 26x + 15? A) x − 5 B) 2x − 5 C) 2x + 3 D) 4x + 3 2) Factor x2 + 5x - 24 A) (x + 8)(x - 3) B) (x + 3)(x - 8) C) (x + 6)(x + 4) D) (x + 2)(x - 12) 3) Factor the polynomial. 8x2 - 50 A) 2(4x - 5)(x - 5) B) 2(2x - 5)(2x - 5) C) 2(2x + 5)(2x + 5) D) 2(2x - 5)(2x + 5) 4) Which binomial is a factor of the polynomial? 3x2 + 7x + 2 A) (x − 1) B) (x − 2) C) (x − 2) D) (3x + 1) 5) Solve. x2 − 5x = 14 A) x = 0, x = 5 B) x = 0, x = −5 C) x = 2, x = −7 D) x = 7, x = −2 6) Factor x2 + 5x - 50 A) (x + 25)(x - 2) B) (x - 5)(x

Step-by-step answer

P Answered by PhD

14

Following are the calculation to the given points:

For point 1:

$\bold{8x^2+26x+15}\\\\\bold{8x^2+(20+6)x+15}\\\\\bold{8x^2+20x+6x+15}\\\\\bold{4x(2x+5)+3(2x+5)}\\\\\bold{(2x+5)(4x+3)}\\\\$

Therefore, the answer is "Option D".

For point 2:

$\bold{x^2 + 5x - 24}\\\\\bold{x^2 + (8-3)x - 24}\\\\\bold{x^2 + 8x-3x - 24}\\\\\bold{x(x + 8)-3(x +8)}\\\\\bold{(x + 8) (x-3)}\\\\$

Therefore, the answer is "Option A".

For point 3:

$\bold{8x2 - 50}\\\\\bold{2(4x2 - 25)}\\\\\bold{2((2x)^2 - 5^2)}\\\\\therefore \ \ x^2-y^2=(x+y) (x-y)\\\\\bold{2((2x - 5)(2x+5)}\\\\$

Therefore, the answer is "Option D".

For point 4:

$\bold{3x^2 + 7x + 2}\\\\\bold{3x^2 +(6+1)x + 2}\\\\\bold{3x^2 +6x+1x + 2}\\\\\bold{3x(x +2)+1(x + 2)}\\\\\bold{(x +2) (3x+1)}\\\\$

Therefore, the answer is "Option D".

For point 5:

$\bold{x^2 - 5x = 14}\\\\\bold{x^2 - 5x -14= 0}\\\\\bold{x^2 - (7-2)x -14= 0}\\\\\bold{x^2 -7x+2x -14= 0}\\\\\bold{x(x -7)+2(x -7)= 0}\\\\\bold{(x -7) (x+2)= 0}\\\\\bold{x -7=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x+2= 0}\\\\\bold{x =7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x= -2}\\\\$

Therefore, the answer is "Option D".

For point 6:

$\bold{x^2 + 5x - 50}\\\\\bold{x^2 + (10-5)x - 50}\\\\\bold{x^2 + 10x-5x - 50}\\\\\bold{x(x+ 10)-5(x +10)}\\\\\bold{(x+ 10)(x -5)}\\\\$

Therefore, the answer is "Option B".

For point 7:

$\bold{16x^2 + 24x + 9}\\\\\bold{16x^2 + (12+12)x + 9}\\\\\bold{16x^2 + 12x+12x + 9}\\\\\bold{4x(4x +3)+3(4x + 3)}\\\\\bold{(4x +3)(4x + 3)}\\\\\bold{(4x +3)^2}\\\\$

Therefore, the answer is "Option A".

For point 8:

$\bold{32x^2 - 50}\\\\\bold{2(16x^2 - 25)}\\\\\bold{2((4x)^2 - (5)^2)}\\\\\bold{2((4x-5)(4x+5))}\\\\$

Therefore, the answer is "Option B".

For point 9:

$\bold{x^2 + 7x - 18}\\\\\bold{x^2 + (9-2)x - 18}\\\\\bold{x^2 + 9x-2x - 18}\\\\\bold{x(x+ 9)-2(x +9)}\\\\\bold{(x+ 9)(x-2)}\\\\$

Therefore, the answer is "Option C".

For point 10:

$\bold{x^2 + 5x - 14}\\\\\bold{x^2 + (7-2)x - 14}\\\\\bold{x^2 + 7x-2x - 14}\\\\\bold{x(x+7)-2(x +7)}\\\\\bold{(x+7)(x -2)}\\\\$

Therefore, the answer is "Option C".

For point 11:

$\bold{25x^2 - 64}\\\\\bold{(5x)^2 - (8)^2}\\\\\bold{(5x-8)(5x+8)}\\\\$

Therefore, the answer is "Option C".

For point 12:

$\bold{x^2 - 81}\\\\\bold{x^2 - 9^2}\\\\\bold{(x - 9)(x+9)}\\\\$

Therefore, the answer is "Option A".

For point 13:

$\bold{8x^2 + 16x + 8 = 0}\\\\\bold{8(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + 2x + 1) = 0}\\\\\bold{(x^2 + x+x + 1) = 0}\\\\\bold{(x(x +1)1(x + 1)) = 0}\\\\\bold{(x +1)(x + 1) = 0}\\\\\bold{(x +1)^2 = 0}\\\\\bold{x +1 = 0}\\\\\bold{x=-1}\\\\$

Therefore, the answer is "Option B".

For point 14:

$\bold{x^2 -x -12 = 0}\\\\\bold{x^2 -(4-3)x -12 = 0}\\\\\bold{x^2 -4x+3x -12 = 0}\\\\\bold{x(x -4)+3(x -4) = 0}\\\\\bold{(x -4) (x+3) = 0}\\\\\bold{(x -4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x+3) = 0}\\\\\bold{x =4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = -3}\\\\$

Therefore, the answer is "Option C".

For point 15:

$\bold{6x^2 + 8x - 28 = 2x^2 + 4}\\\\\bold{6x^2 + 8x - 28 - 2x^2 - 4=0}\\\\\bold{4x^2 + 8x - 32=0}\\\\\bold{4(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + 2x - 8)=0}\\\\\bold{(x^2 + (4-2)x - 8)=0}\\\\\bold{(x^2 + 4x-2x - 8)=0}\\\\\bold{(x(x + 4)-2(x +4))=0}\\\\\bold{(x + 4)(x -2)=0}\\\\\bold{(x + 4)=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (x -2)=0}\\\\\bold{x =-4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x =2}\\\\$

Therefore, the answer is "Option B".

For point 14:

$\bold{6z^2 + 18z}\\\\\bold{6z(z + 3)}\\\\$

Therefore, the answer is "Option B".

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1) Which is a binomial factor of 8x2 + 26x + 15? A) x − 5 B) 2x − 5 C) 2x + 3 D) 4x + 3 2) Facto

1) Which is a binomial factor of 8x2 + 26x + 15? A) x − 5 B) 2x − 5 C) 2x + 3 D) 4x + 3 2) Facto

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