Question

4. Aplicar productos notables 〖(2x-3y)〗^3-(x+5)(x-5)
5. Aplicar productos notables (2x-y)^2-(x+5)^2
6. simplificar (2x-y)(x^2-15x+5)-3x(x+4)

Answer 1

Explicación paso a paso:

4.

$(2x - 3y)^{3} - (x + 5)(x - 5) \\ ( {2x})^{3} -3 \times ( {2x})^{2} (3y) +3 \times (2x)( {3y})^{2} - ( {3y})^{3} \\ 8 {x}^{3} - 36 {x}^{2} y + 54x {y}^{2} - 27 {y}^{3} - ( {x}^{2} - 25) \\ 8 {x}^{3} - 36 {x}^{2} y + 54 x {y}^{2} - 27 {y}^{3} - {x}^{2} + 25$

5.

$(2x - y)^{2} - ( {x + 5})^{2} \\ ({2x})^{2} - 2 \times (2x)(y) + {y}^{2} - ( {x}^{2} + 2 \times (x)(5) + 25) \\ 4 {x}^{2} - 4xy + {y}^{2} - {x}^{2} - 10x - 25 \\ {x}^{2} - 10x - 4xy + {y}^{2} - 25$

6.

$(2x - y)( {x}^{2} - 15x + 5) - 3x(x + 4) \\ 2 {x}^{3} - 30 {x}^{2} +10x - {x}^{2} y + 15xy - 5y - 3 {x}^{2} - 12x \\ 2 {x}^{3} - 33 {x}^{2} - 2x - {x}^{2} y + 15xy - 5y$

Espero haberte ayudado :)

Éxitos.