Question

Me pueden ayudar. Por favor.

Answer 1

Efectúa los siguientes productos:

$1. \\ (x-7)(x+2)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=x,\:b=-7,\:c=x,\:d=2$

$=xx+x\cdot \:2+\left(-7\right)x+\left(-7\right)\cdot \:2$

$=xx+2x-7x-7\cdot \:2$

$=x^2-5x-14$

$2.\\ (m+9)(m-8)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=m,\:b=9,\:c=m,\:d=-8$

$=mm+m\left(-8\right)+9m+9\left(-8\right)$

$=mm-8m+9m-9\cdot \:8$

$=m^2+m-72$

$3.\\ (-x+2)(3-x)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=-x,\:b=2,\:c=3,\:d=-x$

$=\left(-x\right)\cdot \:3+\left(-x\right)\left(-x\right)+2\cdot \:3+2\left(-x\right)$

$=-3x+xx+2\cdot \:3-2x$

$=x^2-5x+6$

$4.\\ (3x+7)(x+4)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=3x,\:b=7,\:c=x,\:d=4$

$=3xx+3x\cdot \:4+7x+7\cdot \:4$

$=3x^2+19x+28$

$5.\\ (2x-5)(3x+2)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=2x,\:b=-5,\:c=3x,\:d=2$

$=2x\cdot \:3x+2x\cdot \:2+\left(-5\right)\cdot \:3x+\left(-5\right)\cdot \:2$

$=2\cdot \:3xx+2\cdot \:2x-5\cdot \:3x-5\cdot \:2$

$=6x^2-11x-10$

$6.\\ \left(5x-4y\right)\left(5x+4y\right)$

$\left(a-b\right)\left(a+b\right)=a^2-b^2$

$a=5x,\:b=4y$

$=\left(5x\right)^2-\left(4y\right)^2$

$=25x^2-16y^2$

$7.\\ (3x+2y)(3x-y)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=3x,\:b=2y,\:c=3x,\:d=-y$

$=3\cdot \:3xx-3xy+2\cdot \:3xy-2yy$

$=9x^2+3xy-2y^2$

$8.\\\left(n^2+4\right)\left(n^2-7\right)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=n^2,\:b=4,\:c=n^2,\:d=-7$

$=n^2n^2+n^2\left(-7\right)+4n^2+4\left(-7\right)$

$=n^4-3n^2-28$

$9.\\ \left(\frac{1}{2}x-3\right)\left(x+\frac{4}{3}\right)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=\frac{x}{2},\:b=-3,\:c=x,\:d=\frac{4}{3}$

$=\frac{x}{2}x+\frac{x}{2}\cdot \frac{4}{3}+\left(-3\right)x+\left(-3\right)\frac{4}{3}$

$=\frac{x}{2}x+\frac{4}{3}\cdot \frac{x}{2}-3x-3\cdot \frac{4}{3}$

$=\frac{3x^2-14x}{6}-4$

$10.\\ \left(\frac{5}{3}x-\frac{1}{2}y\right)\left(\frac{2}{3}x-3y\right)$

$=\left(\frac{5x}{3}-\frac{y}{2}\right)\left(\frac{2}{3}x-3y\right)$

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=\frac{5x}{3},\:b=-\frac{y}{2},\:c=\frac{2x}{3},\:d=-3y$

$=\frac{5x}{3}\cdot \frac{2x}{3}+\frac{5x}{3}\left(-3y\right)+\left(-\frac{y}{2}\right)\frac{2x}{3}+\left(-\frac{y}{2}\right)\left(-3y\right)$

$=\frac{5x}{3}\cdot \frac{2x}{3}-3\cdot \frac{5x}{3}y-\frac{2x}{3}\cdot \frac{y}{2}+3\cdot \frac{y}{2}y$

$=\frac{20x^2-96xy+27y^2}{18}$