Question

resolver productos notables
(2x+4)²=
(4+2y)(5x+3z)=
(x-5)(5x+3z)=
(x+3)³=​

Answer 1

Respuestas:

1.)

$\left(2x+4\right)^2\\\\\mathrm{Aplicar\:la\:formula\:del\:binomio\:al\:cuadrado}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\=\left(2x\right)^2+2\cdot \:2x\cdot \:4+4^2\\\\simplificamos\\\\=4x^2+16x+16$

2.)

$\left(4+2y\right)\left(5x+3z\right)\\\\\mathrm{Aplicar\:la\:propiedad\:distributiva}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\\\=4\cdot \:5x+4\cdot \:3z+2y\cdot \:5x+2y\cdot \:3z\\\\=4\cdot \:5x+4\cdot \:3z+2\cdot \:5yx+2\cdot \:3yz\\\\simplificamos\\\\=20x+12z+10yx+6yz$

3.)

$\left(x-5\right)\left(5x+3z\right)\\\\\mathrm{Aplicar\:la\:propiedad\:distributiva}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\\\=x\cdot \:5x+x\cdot \:3z+\left(-5\right)\cdot \:5x+\left(-5\right)\cdot \:3z\\\\\mathrm{Aplicar\:las\:reglas\:de\:los\:signos}\\+\left(-a\right)=-a\\\\=5xx+3xz-5\cdot \:5x-5\cdot \:3z\\\\simplificamos\\\\=5x^2+3xz-25x-15z$

4.)

$\left(x+3\right)^3\\\\\mathrm{Aplicar\:la\:fórmula\:del\:binomio\:al\:cubo}:\quad \left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\\\\=x^3+3x^2\cdot \:3+3x\cdot \:3^2+3^3\\\\simplificamos\\\\=x^3+9x^2+27x+27$

espero que te ayude;-)