How to find the product of sum and difference of two binomials with the same terms and opposite signs?

(a + b) (a – b) = a(a – b) + b (a – b)

= a

= a

Therefore (a + b) (a – b) = a

(First term + Second term) (First term – Second term) = (First term)

**It is stated as:** The
product of the binomial sum and difference is equal to the square of the first
term minus the square of the second term.

Worked-out examples on the product of sum and difference of two binomials:

We know (a + b) (a – b) = a

Here a = 2x and b= 7y

= (2x)

= 4x

Therefore, (2x + 7y)(2x – 7y) = 4x

We know a

Here a = 50, b = 49

= (50 + 49) (50 – 49)

= 99 × 1

= 99

Therefore, 50

63 × 57 = (60 + 3) (60 – 3)

We know (a + b) (a – b) = a

= (60)

= 3600 – 9

= 3591

Therefore, 63 × 57 = 3591

We know a

Here a = 23 and b = 17

Therefore 23

(23 + 17)(23 – 17) = 6x

40 × 6 = 6x

240 = 6x

6x/6 = 240/6

Therefore, x = 40

43 × 37 = (40 + 3)( 40 – 3)

We know (a + b) (a – b) = a

Here a = 40 and b = 3

= (40)

= 1600 – 9

= 1591

Therefore, 43 × 37 = 1591

Thus, the product of sum and difference of two binomials is equal to the square of the first term minus the square of the second term.

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