Question

Resolve the following into factors: 16a² – 24a + 9 using this identities (a – b)² = a² – 2ab + b²​

Answer 1

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Answer 2

Answer:

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Step-by-step explanation:

An identity is true only for certain values of its variables. An equation is not an identity.

The following are the identities

(a + b)² = a² + 2ab + b²  

(a – b)² = a² – 2ab + b²  

(a – b)(a + b) = a² – b²

Another useful identity is

(x + a) (x + b) = x² + (a + b) x + ab

If the given expression is the difference of two squares we use the formula

a² –b² = (a+b)(a-b)

 

• The above four identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers and so on.

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Solution:

1) 71²

= (70+1)²

= 70²+ 2×70×1+ 1²               [(a + b)² = a² + 2ab + b² ]

= 4900 + 140 +1

= 5041

2) 99²

= (100 -1)²

= 100²- 2×100×1 + 1²               [(a – b)² = a² – 2ab + b² ]

= 10000 - 200 + 1

= 9801

3) 102²= (100 + 2)²

= 100²+ 2×100 ×2+ 2²            [(a + b)² = a² + 2ab + b² ]

= 10000 + 400 + 4

= 10404

4) 998²= (1000 - 2)²

= 1000² - 2×1000×2 + 2²                         [(a – b)² = a² – 2ab + b² ]

= 1000000 - 4000 + 4

= 996004

5) 5.2²= (5 + 0.2)²

= 5² + 2×5×0.2 + 0.2²                [(a + b)² = a² + 2ab + b² ]

= 25 + 2 + 0.04

= 27.04

6) = (300 - 3 )(300 + 3)

= 300²- 3²

= 90000 - 9

= 89991

7) = (80 - 2)(80 + 2)

= 80² - 2²                                   [(a – b)(a + b) = a² – b²]

= 6400 - 4

= 6396

8) 8.9²= (9 - 0.1)²

= 9² - 2×9×0.1 + 0.1²                   [ [(a – b)² = a² – 2ab + b² ]]

= 81 - 1.8 + 0.01

= 79.21

9)  

1.05 × 9.5

1.05 × .95 x 10

= (1+ 0.05)(1 - 0.05) x10             [(a – b)(a + b) = a² – b²[

= [1² - 0.05²] x 10

= [1 - 0.0025] x10

= 0.9975 x 10

= 9.975

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Hope this will help you.....