Question

taller
1. (2x + 3y + 4) 2 =
2. (5m + 3n – 2) 2 =
3. (x 3 +2 y 2 + 3z) 2 =
4. (x + 3)(x +6)=
5. (2x 2 + 5)(2x 2 +4)=
6. (7m + 8)(7m -3)=

ayuda, necesito el procedimiento de cada una

Answer 1

RESOLVER:

a) $\left(2x+3y+4\right)^2$

$\left(2x+3y+4\right)^2=\left(2x+3y+4\right)\left(2x+3y+4\right)$

$=\left(2x+3y+4\right)\left(2x+3y+4\right)$

$\left(2x+3y+4\right)\left(2x+3y+4\right)=2x\cdot \:2x+2x\cdot \:3y+2x\cdot \:4+3y\cdot \:2x+3y\cdot \:3y+3y\cdot \:4+4\cdot \:2x+4\cdot \:3y+4\cdot \:4$

$=2x\cdot \:2x+2x\cdot \:3y+2x\cdot \:4+3y\cdot \:2x+3y\cdot \:3y+3y\cdot \:4+4\cdot \:2x+4\cdot \:3y+4\cdot \:4$

Simplificamos

$2x\cdot \:2x+2x\cdot \:3y+2x\cdot \:4+3y\cdot \:2x+3y\cdot \:3y+3y\cdot \:4+4\cdot \:2x+4\cdot \:3y+4\cdot \:4$

$\boxed{=4x^2+12xy+16x+9y^2+24y+16}$

b) $\left(5m+3n-2\right)^2$

$\left(5m+3n-2\right)^2=\left(5m+3n-2\right)\left(5m+3n-2\right)$

$=\left(5m+3n-2\right)\left(5m+3n-2\right)$

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

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

Simplificamos

$5m\cdot \:5m+5m\cdot \:3n+5m\left(-2\right)+3n\cdot \:5m+3n\cdot \:3n+3n\left(-2\right)-2\cdot \:5m-2\cdot \:3n-2\left(-2\right)$

$\boxed{=25m^2+30mn-20m+9n^2-12n+4}$

c) $\left(x^3+2y^2+3z\right)^2$

$\left(x^3+2y^2+3z\right)^2=\left(x^3+2y^2+3z\right)\left(x^3+2y^2+3z\right)$

$=\left(x^3+2y^2+3z\right)\left(x^3+2y^2+3z\right)$

$\left(x^3+2y^2+3z\right)\left(x^3+2y^2+3z\right)=x^3x^3+x^3\cdot \:2y^2+x^3\cdot \:3z+2y^2x^3+2y^2\cdot \:2y^2+2y^2\cdot \:3z+3zx^3+3z\cdot \:2y^2+3zx^3+3z\cdot \:2y^2+3z\cdot3z$

$=x^3x^3+x^3\cdot \:2y^2+x^3\cdot \:3z+2y^2x^3+2y^2\cdot \:2y^2+2y^2\cdot \:3z+3zx^3+3z\cdot \:2y^2+3z\cdot \:3z$

Simplificamos

$x^3x^3+x^3\cdot \:2y^2+x^3\cdot \:3z+2y^2x^3+2y^2\cdot \:2y^2+2y^2\cdot \:3z+3zx^3+3z\cdot \:2y^2+3z\cdot \:3z$

$\boxed{=x^6+4y^4+2x^3y^2+6x^3z+9z^2+2y^2x^3+12y^2z}$

d) $\left(x+3\right)\left(x+6\right)$

$\left(x+3\right)\left(x+6\right)=xx+x\cdot \:6+3x+3\cdot \:6$

$=xx+x\cdot \:6+3x+3\cdot \:6$

Simplificamos

$xx+x\cdot \:6+3x+3\cdot \:6:x^2+9x+18$

$\boxed{=x^2+9x+18}$

e) $\left(2x^2+5\right)\left(2x^2+4\right)$

$\left(2x^2+5\right)\left(2x^2+4\right)=2x^2\cdot \:2x^2+2x^2\cdot \:4+5\cdot \:2x^2+5\cdot \:4$

$=2x^2\cdot \:2x^2+2x^2\cdot \:4+5\cdot \:2x^2+5\cdot \:4$

Simplificamos

$2x^2\cdot \:2x^2+2x^2\cdot \:4+5\cdot \:2x^2+5\cdot \:4$

$\boxed{=4x^4+18x^2+20}$

f) $\left(7m+8\right)\left(7m-3\right)$

$\left(7m+8\right)\left(7m-3\right)=7m\cdot \:7m+7m\left(-3\right)+8\cdot \:7m+8\left(-3\right)$

$=7m\cdot \:7m+7m\left(-3\right)+8\cdot \:7m+8\left(-3\right)$

Simplificamos

$7m\cdot \:7m+7m\left(-3\right)+8\cdot \:7m+8\left(-3\right)$

$\boxed{=49m^2+35m-24}$

MUCHA SUERTE....