What is (2a+3b-5c+7d)^2-(2a-3b+5c-7d)^2 ?

The solution to (2a+3b-5c+7d)^2-(2a-3b+5c-7d)^2 is 24ab-40ac+56ad

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simplify (2a+3b-5c+7d)^2-(2a-3b+5c-7d)^2

simplify

(2 a + 3 b - 5 c + 7 d)^{2} - (2 a - 3 b + 5 c - 7 d)^{2}

24 ab - 40 a c + 56 a d

Solution steps

(2 a + 3 b - 5 c + 7 d)^{2} - (2 a - 3 b + 5 c - 7 d)^{2}

Expand

(2 a + 3 b - 5 c + 7 d)^{2} : 4 a^{2} + 12 ab - 20 a c + 28 a d + 9 b^{2} - 30 b c + 42 b d + 25 c^{2} - 70 c d + 49 d^{2}

= 4 a^{2} + 12 ab - 20 a c + 28 a d + 9 b^{2} - 30 b c + 42 b d + 25 c^{2} - 70 c d + 49 d^{2} - (2 a - 3 b + 5 c - 7 d)^{2}

Expand

- (2 a - 3 b + 5 c - 7 d)^{2} : - 4 a^{2} + 12 ab - 20 a c + 28 a d - 9 b^{2} + 30 b c - 42 b d - 25 c^{2} + 70 c d - 49 d^{2}

= 4 a^{2} + 12 ab - 20 a c + 28 a d + 9 b^{2} - 30 b c + 42 b d + 25 c^{2} - 70 c d + 49 d^{2} - 4 a^{2} + 12 ab - 20 a c + 28 a d - 9 b^{2} + 30 b c - 42 b d - 25 c^{2} + 70 c d - 49 d^{2}

Group like terms

= 4 a^{2} - 4 a^{2} + 12 ab + 12 ab - 20 a c - 20 a c + 28 a d + 28 a d + 9 b^{2} - 9 b^{2} - 30 b c + 30 b c + 42 b d - 42 b d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

4 a^{2} - 4 a^{2} = 0

= 12 ab + 12 ab - 20 a c - 20 a c + 28 a d + 28 a d + 9 b^{2} - 9 b^{2} - 30 b c + 30 b c + 42 b d - 42 b d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

12 ab + 12 ab = 24 ab

= 24 ab - 20 a c - 20 a c + 28 a d + 28 a d + 9 b^{2} - 9 b^{2} - 30 b c + 30 b c + 42 b d - 42 b d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

- 20 a c - 20 a c = - 40 a c

= 24 ab - 40 a c + 28 a d + 28 a d + 9 b^{2} - 9 b^{2} - 30 b c + 30 b c + 42 b d - 42 b d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

28 a d + 28 a d = 56 a d

= 24 ab - 40 a c + 56 a d + 9 b^{2} - 9 b^{2} - 30 b c + 30 b c + 42 b d - 42 b d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

9 b^{2} - 9 b^{2} = 0

= 24 ab - 40 a c + 56 a d - 30 b c + 30 b c + 42 b d - 42 b d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

- 30 b c + 30 b c = 0

= 24 ab - 40 a c + 56 a d + 42 b d - 42 b d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

42 b d - 42 b d = 0

= 24 ab - 40 a c + 56 a d + 25 c^{2} - 25 c^{2} - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

25 c^{2} - 25 c^{2} = 0

= 24 ab - 40 a c + 56 a d - 70 c d + 70 c d + 49 d^{2} - 49 d^{2}

Add similar elements:

- 70 c d + 70 c d = 0

= 24 ab - 40 a c + 56 a d + 49 d^{2} - 49 d^{2}

Add similar elements:

49 d^{2} - 49 d^{2} = 0

= 24 ab - 40 a c + 56 a d

(4 x - 3) (2 x + 1) - 8 x (x - 2)

(- 5 - y) 2

\frac{( x ^{5} )}{( x ^{- 3} )}

\frac{( p ^{3} \cdot ( q - r ) ^{3} - q ^{3} \cdot ( p - r ) ^{3} - r ^{3} \cdot ( q - p ) ^{3} )}{( ( p - q ) ( r - q ) ( p - r ) )}

\frac{x ^{1}}{y}

What is (2a+3b-5c+7d)^2-(2a-3b+5c-7d)^2 ?
The solution to (2a+3b-5c+7d)^2-(2a-3b+5c-7d)^2 is 24ab-40ac+56ad