simplificar 49(2x+3y)^2-70(4x^2-9y^2)+25(2x-3y)^2

Solução

simplificar

49 \cdot (2 x + 3 y)^{2} - 70 (4 x^{2} - 9 y^{2}) + 25 \cdot (2 x - 3 y)^{2}

16 x^{2} + 288 x y + 1296 y^{2}

Passos da solução

49 (2 x + 3 y)^{2} - 70 (4 x^{2} - 9 y^{2}) + 25 (2 x - 3 y)^{2}

Expandir

49 (2 x + 3 y)^{2} : 196 x^{2} + 588 x y + 441 y^{2}

= 196 x^{2} + 588 x y + 441 y^{2} - 70 (4 x^{2} - 9 y^{2}) + 25 (2 x - 3 y)^{2}

Expandir

- 70 (4 x^{2} - 9 y^{2}) : - 280 x^{2} + 630 y^{2}

= 196 x^{2} + 588 x y + 441 y^{2} - 280 x^{2} + 630 y^{2} + 25 (2 x - 3 y)^{2}

Expandir

25 (2 x - 3 y)^{2} : 100 x^{2} - 300 x y + 225 y^{2}

= 196 x^{2} + 588 x y + 441 y^{2} - 280 x^{2} + 630 y^{2} + 100 x^{2} - 300 x y + 225 y^{2}

Agrupar termos semelhantes

= 196 x^{2} - 280 x^{2} + 100 x^{2} + 588 x y - 300 x y + 441 y^{2} + 630 y^{2} + 225 y^{2}

Somar elementos similares:

196 x^{2} - 280 x^{2} + 100 x^{2} = 16 x^{2}

= 16 x^{2} + 588 x y - 300 x y + 441 y^{2} + 630 y^{2} + 225 y^{2}

Somar elementos similares:

588 x y - 300 x y = 288 x y

= 16 x^{2} + 288 x y + 441 y^{2} + 630 y^{2} + 225 y^{2}

Somar elementos similares:

441 y^{2} + 630 y^{2} + 225 y^{2} = 1296 y^{2}

= 16 x^{2} + 288 x y + 1296 y^{2}

s im pl i f y (x - 1) (x + 3) - (\frac{( 2 x - 2 )}{( x + 2 )})

s im pl i f y \frac{( a ^{3} )}{( ( a - b ) ( a - c ) )} + \frac{( b ^{3} )}{( ( b - a ) ( b - c ) )} + \frac{( c ^{3} )}{( ( c - a ) ( c - b ) )}

f a c t or x^{6} - 15625

e x p an d (b^{x + 1} - 3) (b^{x + 1} - 1)

s im pl i f y n + 1 + (- 2) n