Inicio › Matemáticas 1 › Expresiones algebraicas

Matemáticas 1 · Tema 5

Expresiones algebraicas

Ejemplos

4[(+3x−2)(5−3x)+2x]−4=4[15x−9x2−10+6x+2x]−4=60x−36x2−40+24x+8x−4=−36x2+92x−44\begin{aligned} 4[(+3x-2)(5-3x)+2x]-4 &= \\ 4[15x-9x^2-10+6x+2x]-4 &= \\ 60x-36x^2-40+24x+8x-4 &= \\ \mathbf{-36x^2+92x-44} & \end{aligned}
2(−3x+1)2+2(−4+3x)−2=2(−3x+1)(−3x+1)−8+6x−2=2(9x2−3x−3x+1)−8+6x−2=2(9x2−6x+1)−8+6x−2=18x2−12x+2−8+6x−2=18x2−6x−8\begin{aligned} 2(-3x+1)^2+2(-4+3x)-2 &= \\ 2(-3x+1)(-3x+1)-8+6x-2 &= \\ 2(9x^2-3x-3x+1)-8+6x-2 &= \\ 2(9x^2-6x+1)-8+6x-2 &= \\ 18x^2-12x+2-8+6x-2 &= \\ \mathbf{18x^2-6x-8} & \end{aligned}

Ejercicios

Bloque 1
4[(−4x+5)(2−5x)+6x]−3=4[(-4x+5)(2-5x)+6x]-3=
2[(−3x+2)(4−5x)+3x]−5=2[(-3x+2)(4-5x)+3x]-5=
3[(−2x+3)(5−4x)+2x]−5=3[(-2x+3)(5-4x)+2x]-5=
5[(2x−3)(1−3x)+4x]−2=5[(2x-3)(1-3x)+4x]-2=
3[(−5x+2)(3−2x)+7x]−4=3[(-5x+2)(3-2x)+7x]-4=
4[(3x−2)(1−4x)+5x]−3=4[(3x-2)(1-4x)+5x]-3=
Bloque 2
4(−3x+2)2+3(−1+5x)−6=4(-3x+2)^2+3(-1+5x)-6=
5(2x−1)2+4(−3+6x)−3=5(2x-1)^2+4(-3+6x)-3=
5(−4x+3)2−2(3−2x)−4=5(-4x+3)^2-2(3-2x)-4=
2(−2x+4)2+3(−5x+3)−1=2(-2x+4)^2+3(-5x+3)-1=
4(3x−2)2+2(−4+3x)−7=4(3x-2)^2+2(-4+3x)-7=
3(−2x+5)2+4(−3+2x)−8=3(-2x+5)^2+4(-3+2x)-8=

Ejercicios resueltos

▼
4[(−4x+5)(2−5x)+6x]−3=4[−8x+20x2+10−25x+6x]−3=−32x+80x2+40−100x+24x−3=80x2−108x+37\begin{aligned} 4[(-4x+5)(2-5x)+6x]-3 &= \\ 4[-8x+20x^2+10-25x+6x]-3 &= \\ -32x+80x^2+40-100x+24x-3 &= \\ \mathbf{80x^2-108x+37} & \end{aligned}
2[(−3x+2)(4−5x)+3x]−5=2[−12x+15x2+8−10x+3x]−5=−24x+30x2+16−20x+6x−5=30x2−38x+11\begin{aligned} 2[(-3x+2)(4-5x)+3x]-5 &= \\ 2[-12x+15x^2+8-10x+3x]-5 &= \\ -24x+30x^2+16-20x+6x-5 &= \\ \mathbf{30x^2-38x+11} & \end{aligned}
3[(−2x+3)(5−4x)+2x]−5=3[−10x+8x2+15−12x+2x]−5=−30x+24x2+45−36x+6x−5=24x2−60x+40\begin{aligned} 3[(-2x+3)(5-4x)+2x]-5 &= \\ 3[-10x+8x^2+15-12x+2x]-5 &= \\ -30x+24x^2+45-36x+6x-5 &= \\ \mathbf{24x^2-60x+40} & \end{aligned}
5[(2x−3)(1−3x)+4x]−2=5[2x−6x2−3+9x+4x]−2=10x−30x2−15+45x+20x−2=−30x2+75x−17\begin{aligned} 5[(2x-3)(1-3x)+4x]-2 &= \\ 5[2x-6x^2-3+9x+4x]-2 &= \\ 10x-30x^2-15+45x+20x-2 &= \\ \mathbf{-30x^2+75x-17} & \end{aligned}
3[(−5x+2)(3−2x)+7x]−4=3[10x2−19x+6+7x]−4=3[10x2−12x+6]−4=30x2−36x+18−4=30x2−36x+14\begin{aligned} 3[(-5x+2)(3-2x)+7x]-4 &= \\ 3[10x^2-19x+6+7x]-4 &= \\ 3[10x^2-12x+6]-4 &= \\ 30x^2-36x+18-4 &= \\ \mathbf{30x^2-36x+14} & \end{aligned}
4[(3x−2)(1−4x)+5x]−3=4[3x−12x2−2+8x+5x]−3=12x−48x2−8+32x+20x−3=−48x2+64x−11\begin{aligned} 4[(3x-2)(1-4x)+5x]-3 &= \\ 4[3x-12x^2-2+8x+5x]-3 &= \\ 12x-48x^2-8+32x+20x-3 &= \\ \mathbf{-48x^2+64x-11} & \end{aligned}
4(−3x+2)2+3(−1+5x)−6=4(−3x+2)(−3x+2)−3+15x−6=4(9x2−6x−6x+4)−3+15x−6=4(9x2−12x+4)−3+15x−6=36x2−48x+16−3+15x−6=36x2−33x+7\begin{aligned} 4(-3x+2)^2+3(-1+5x)-6 &= \\ 4(-3x+2)(-3x+2)-3+15x-6 &= \\ 4(9x^2-6x-6x+4)-3+15x-6 &= \\ 4(9x^2-12x+4)-3+15x-6 &= \\ 36x^2-48x+16-3+15x-6 &= \\ \mathbf{36x^2-33x+7} & \end{aligned}
5(2x−1)2+4(−3+6x)−3=5(2x−1)(2x−1)−12+24x−3=5(4x2−2x−2x+1)−12+24x−3=5(4x2−4x+1)−12+24x−3=20x2−20x+5−12+24x−3=20x2+4x−10\begin{aligned} 5(2x-1)^2+4(-3+6x)-3 &= \\ 5(2x-1)(2x-1)-12+24x-3 &= \\ 5(4x^2-2x-2x+1)-12+24x-3 &= \\ 5(4x^2-4x+1)-12+24x-3 &= \\ 20x^2-20x+5-12+24x-3 &= \\ \mathbf{20x^2+4x-10} & \end{aligned}
5(−4x+3)2−2(3−2x)−4=5(−4x+3)(−4x+3)−6+4x−4=5(16x2−12x−12x+9)−6+4x−4=5(16x2−24x+9)−6+4x−4=80x2−120x+45−6+4x−4=80x2−116x+35\begin{aligned} 5(-4x+3)^2-2(3-2x)-4 &= \\ 5(-4x+3)(-4x+3)-6+4x-4 &= \\ 5(16x^2-12x-12x+9)-6+4x-4 &= \\ 5(16x^2-24x+9)-6+4x-4 &= \\ 80x^2-120x+45-6+4x-4 &= \\ \mathbf{80x^2-116x+35} & \end{aligned}
2(−2x+4)2+3(−5x+3)−1=2(−2x+4)(−2x+4)−15x+9−1=2(4x2−8x−8x+16)−15x+9−1=2(4x2−16x+16)−15x+9−1=8x2−32x+32−15x+9−1=8x2−47x+40\begin{aligned} 2(-2x+4)^2+3(-5x+3)-1 &= \\ 2(-2x+4)(-2x+4)-15x+9-1 &= \\ 2(4x^2-8x-8x+16)-15x+9-1 &= \\ 2(4x^2-16x+16)-15x+9-1 &= \\ 8x^2-32x+32-15x+9-1 &= \\ \mathbf{8x^2-47x+40} & \end{aligned}
4(3x−2)2+2(−4+3x)−7=4(9x2−12x+4)−8+6x−7=36x2−48x+16−8+6x−7=36x2−42x+1\begin{aligned} 4(3x-2)^2+2(-4+3x)-7 &= \\ 4(9x^2-12x+4)-8+6x-7 &= \\ 36x^2-48x+16-8+6x-7 &= \\ \mathbf{36x^2-42x+1} & \end{aligned}
3(−2x+5)2+4(−3+2x)−8=3(−2x+5)(−2x+5)−12+8x−8=3(4x2−10x−10x+25)−12+8x−8=3(4x2−20x+25)−12+8x−8=12x2−60x+75−12+8x−8=12x2−52x+55\begin{aligned} 3(-2x+5)^2+4(-3+2x)-8 &= \\ 3(-2x+5)(-2x+5)-12+8x-8 &= \\ 3(4x^2-10x-10x+25)-12+8x-8 &= \\ 3(4x^2-20x+25)-12+8x-8 &= \\ 12x^2-60x+75-12+8x-8 &= \\ \mathbf{12x^2-52x+55} & \end{aligned}

Ejercicios extra 1

▼
Bloque A
3[(2x+3)(4−x)+5x]−2=3[(2x+3)(4-x)+5x]-2=
4[(−3x+1)(5−2x)+3x]+1=4[(-3x+1)(5-2x)+3x]+1=
2[(x+5)(3−2x)+4x]−3=2[(x+5)(3-2x)+4x]-3=
5[(−x+3)(2−4x)+2x]−1=5[(-x+3)(2-4x)+2x]-1=
2[(4x−1)(2−3x)+5x]−6=2[(4x-1)(2-3x)+5x]-6=
5[(2x−4)(3−x)+2x]−1=5[(2x-4)(3-x)+2x]-1=
Bloque B
2(x−4)2+3(2x+5)−7=2(x-4)^2+3(2x+5)-7=
4(3x−1)2+2(2−5x)−5=4(3x-1)^2+2(2-5x)-5=
3(2x+5)2−4(3−x)+2=3(2x+5)^2-4(3-x)+2=
4(−x+2)2+5(−3+4x)−6=4(-x+2)^2+5(-3+4x)-6=
5(−2x+3)2+4(2x−5)−3=5(-2x+3)^2+4(2x-5)-3=
2(−4x+3)2+5(2x−1)−7=2(-4x+3)^2+5(2x-1)-7=
← Monomios Gráfica con tabulación →