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) [tex]\left(2x+3y+4\right)^2[/tex]

[tex]\left(2x+3y+4\right)^2=\left(2x+3y+4\right)\left(2x+3y+4\right)[/tex]

[tex]=\left(2x+3y+4\right)\left(2x+3y+4\right)[/tex]

[tex]\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[/tex]

[tex]=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[/tex]

Simplificamos

[tex]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[/tex]

[tex]\boxed{=4x^2+12xy+16x+9y^2+24y+16}[/tex]

b) [tex]\left(5m+3n-2\right)^2[/tex]

[tex]\left(5m+3n-2\right)^2=\left(5m+3n-2\right)\left(5m+3n-2\right)[/tex]

[tex]=\left(5m+3n-2\right)\left(5m+3n-2\right)[/tex]

[tex]\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)[/tex]

[tex]=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)[/tex]

Simplificamos

[tex]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)[/tex]

[tex]\boxed{=25m^2+30mn-20m+9n^2-12n+4}[/tex]

c) [tex]\left(x^3+2y^2+3z\right)^2[/tex]

[tex]\left(x^3+2y^2+3z\right)^2=\left(x^3+2y^2+3z\right)\left(x^3+2y^2+3z\right)[/tex]

[tex]=\left(x^3+2y^2+3z\right)\left(x^3+2y^2+3z\right)[/tex]

[tex]\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[/tex]

[tex]=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[/tex]

Simplificamos

[tex]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[/tex]

[tex]\boxed{=x^6+4y^4+2x^3y^2+6x^3z+9z^2+2y^2x^3+12y^2z}[/tex]

d) [tex]\left(x+3\right)\left(x+6\right)[/tex]

[tex]\left(x+3\right)\left(x+6\right)=xx+x\cdot \:6+3x+3\cdot \:6[/tex]

[tex]=xx+x\cdot \:6+3x+3\cdot \:6[/tex]

Simplificamos

[tex]xx+x\cdot \:6+3x+3\cdot \:6:x^2+9x+18[/tex]

[tex]\boxed{=x^2+9x+18}[/tex]

e) [tex]\left(2x^2+5\right)\left(2x^2+4\right)[/tex]

[tex]\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[/tex]

[tex]=2x^2\cdot \:2x^2+2x^2\cdot \:4+5\cdot \:2x^2+5\cdot \:4[/tex]

Simplificamos

[tex]2x^2\cdot \:2x^2+2x^2\cdot \:4+5\cdot \:2x^2+5\cdot \:4[/tex]

[tex]\boxed{=4x^4+18x^2+20}[/tex]

f) [tex]\left(7m+8\right)\left(7m-3\right)[/tex]

[tex]\left(7m+8\right)\left(7m-3\right)=7m\cdot \:7m+7m\left(-3\right)+8\cdot \:7m+8\left(-3\right)[/tex]

[tex]=7m\cdot \:7m+7m\left(-3\right)+8\cdot \:7m+8\left(-3\right)[/tex]

Simplificamos

[tex]7m\cdot \:7m+7m\left(-3\right)+8\cdot \:7m+8\left(-3\right)[/tex]

[tex]\boxed{=49m^2+35m-24}[/tex]

MUCHA SUERTE....