6. $$ 121 \mathrm{a}^{6}-144 \mathrm{~b}^{\mathrm{a}} $$ 7. $$ \mathrm{x}^{3}-27 $$ 8. $$ 8 \mathrm{y}^{3}+125 $$ 9. $$ 216 \mathrm{a}^{9}-343 \mathrm{~b}^{6} $$ 10. $$ \mathrm{x}^{2}-10 \mathrm{x}+25 $$ 11. $$ 36 \mathrm{y}^{2}+60 \mathrm{y}+25 $$ 12. $$ 81 \mathrm{a}^{4}-108 \mathrm{a}^{2} \mathrm{~b}+36 \mathrm{~b}^{2} $$ 13. $$ \mathrm{x}^{2}+9 \mathrm{x}+20 $$ 14. $$ \mathrm{x}^{2}-3 \mathrm{x}-40 $$ 15. $$ \mathrm{x}^{2}-15 \mathrm{x}+56 $$ 16. $$ 3 \mathrm{x}^{2}+10 \mathrm{x}+7 $$ 17. $$ 5 \mathrm{x}^{2}-17 \mathrm{x}+6 $$ 18. $$ 18 \mathrm{x}^{2}-33 \mathrm{x}+14 $$

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UpStudy AI · Accepted Answer

Factor the expression by following steps:
- step0: Factor:
  $$18x^{2}-33x+14$$
- step1: Rewrite the expression:
  $$18x^{2}+\left(-21-12ight)x+14$$
- step2: Calculate:
  $$18x^{2}-21x-12x+14$$
- step3: Rewrite the expression:
  $$3x	imes 6x-3x	imes 7-2	imes 6x+2	imes 7$$
- step4: Factor the expression:
  $$3x\left(6x-7ight)-2\left(6x-7ight)$$
- step5: Factor the expression:
  $$\left(3x-2ight)\left(6x-7ight)$$
Factor the expression $$ x^{2}-3 x-40 $$.
Factor the expression by following steps:
- step0: Factor:
  $$x^{2}-3x-40$$
- step1: Rewrite the expression:
  $$x^{2}+\left(5-8ight)x-40$$
- step2: Calculate:
  $$x^{2}+5x-8x-40$$
- step3: Rewrite the expression:
  $$x	imes x+x	imes 5-8x-8	imes 5$$
- step4: Factor the expression:
  $$x\left(x+5ight)-8\left(x+5ight)$$
- step5: Factor the expression:
  $$\left(x-8ight)\left(x+5ight)$$
Factor the expression $$ 36 y^{2}+60 y+25 $$.
Factor the expression by following steps:
- step0: Factor:
  $$36y^{2}+60y+25$$
- step1: Factor the expression:
  $$\left(6y+5ight)^{2}$$
Factor the expression $$ x^{2}-15 x+56 $$.
Factor the expression by following steps:
- step0: Factor:
  $$x^{2}-15x+56$$
- step1: Rewrite the expression:
  $$x^{2}+\left(-7-8ight)x+56$$
- step2: Calculate:
  $$x^{2}-7x-8x+56$$
- step3: Rewrite the expression:
  $$x	imes x-x	imes 7-8x+8	imes 7$$
- step4: Factor the expression:
  $$x\left(x-7ight)-8\left(x-7ight)$$
- step5: Factor the expression:
  $$\left(x-8ight)\left(x-7ight)$$
Factor the expression $$ 3 x^{2}+10 x+7 $$.
Factor the expression by following steps:
- step0: Factor:
  $$3x^{2}+10x+7$$
- step1: Rewrite the expression:
  $$3x^{2}+\left(7+3ight)x+7$$
- step2: Calculate:
  $$3x^{2}+7x+3x+7$$
- step3: Rewrite the expression:
  $$x	imes 3x+x	imes 7+3x+7$$
- step4: Factor the expression:
  $$x\left(3x+7ight)+3x+7$$
- step5: Factor the expression:
  $$\left(x+1ight)\left(3x+7ight)$$
Factor the expression $$ 8 y^{3}+125 $$.
Factor the expression by following steps:
- step0: Factor:
  $$8y^{3}+125$$
- step1: Rewrite the expression:
  $$\left(2yight)^{3}+5^{3}$$
- step2: Factor the expression:
  $$\left(2y+5ight)\left(\left(2yight)^{2}-2y	imes 5+5^{2}ight)$$
- step3: Evaluate:
  $$\left(2y+5ight)\left(4y^{2}-10y+25ight)$$
Factor the expression $$ x^{3}-27 $$.
Factor the expression by following steps:
- step0: Factor:
  $$x^{3}-27$$
- step1: Rewrite the expression:
  $$x^{3}-3^{3}$$
- step2: Factor the expression:
  $$\left(x-3ight)\left(x^{2}+x	imes 3+3^{2}ight)$$
- step3: Reorder the terms:
  $$\left(x-3ight)\left(x^{2}+3x+9ight)$$
Factor the expression $$ 5 x^{2}-17 x+6 $$.
Factor the expression by following steps:
- step0: Factor:
  $$5x^{2}-17x+6$$
- step1: Rewrite the expression:
  $$5x^{2}+\left(-2-15ight)x+6$$
- step2: Calculate:
  $$5x^{2}-2x-15x+6$$
- step3: Rewrite the expression:
  $$x	imes 5x-x	imes 2-3	imes 5x+3	imes 2$$
- step4: Factor the expression:
  $$x\left(5x-2ight)-3\left(5x-2ight)$$
- step5: Factor the expression:
  $$\left(x-3ight)\left(5x-2ight)$$
Factor the expression $$ 81 a^{4}-108 a^{2} b+36 b^{2 $$.
Factor the expression by following steps:
- step0: Factor:
  $$81a^{4}-108a^{2}b+36b^{2}$$
- step1: Factor the expression:
  $$9\left(3a^{2}-2bight)^{2}$$
Factor the expression $$ x^{2}+9 x+20 $$.
Factor the expression by following steps:
- step0: Factor:
  $$x^{2}+9x+20$$
- step1: Rewrite the expression:
  $$x^{2}+\left(5+4ight)x+20$$
- step2: Calculate:
  $$x^{2}+5x+4x+20$$
- step3: Rewrite the expression:
  $$x	imes x+x	imes 5+4x+4	imes 5$$
- step4: Factor the expression:
  $$x\left(x+5ight)+4\left(x+5ight)$$
- step5: Factor the expression:
  $$\left(x+4ight)\left(x+5ight)$$
Factor the expression $$ x^{2}-10 x+25 $$.
Factor the expression by following steps:
- step0: Factor:
  $$x^{2}-10x+25$$
- step1: Factor the expression:
  $$\left(x-5ight)^{2}$$
Factor the expression $$ 216 a^{9}-343 b^{6} $$.
Factor the expression by following steps:
- step0: Factor:
  $$216a^{9}-343b^{6}$$
- step1: Rewrite the expression:
  $$\left(6a^{3}ight)^{3}-\left(7b^{2}ight)^{3}$$
- step2: Factor the expression:
  $$\left(6a^{3}-7b^{2}ight)\left(\left(6a^{3}ight)^{2}+6a^{3}	imes 7b^{2}+\left(7b^{2}ight)^{2}ight)$$
- step3: Evaluate:
  $$\left(6a^{3}-7b^{2}ight)\left(36a^{6}+42a^{3}b^{2}+49b^{4}ight)$$
Aquí están las factorizaciones de las expresiones proporcionadas:

6. $$ 121 a^{6}-144 b^{a} $$  
   No se pudo encontrar un resultado para esta expresión.

7. $$ x^{3}-27 $$  
   Factorización: $$ (x-3)(x^{2}+3x+9) $$

8. $$ 8 y^{3}+125 $$  
   Factorización: $$ (2y+5)(4y^{2}-10y+25) $$

9. $$ 216 a^{9}-343 b^{6} $$  
   Factorización: $$ (6a^{3}-7b^{2})(36a^{6}+42a^{3}b^{2}+49b^{4}) $$

10. $$ x^{2}-10 x+25 $$  
    Factorización: $$ (x-5)^{2} $$

11. $$ 36 y^{2}+60 y+25 $$  
    Factorización: $$ (6y+5)^{2} $$

12. $$ 81 a^{4}-108 a^{2} b+36 b^{2} $$  
    Factorización: $$ 9(3a^{2}-2b)^{2} $$

13. $$ x^{2}+9 x+20 $$  
    Factorización: $$ (x+4)(x+5) $$

14. $$ x^{2}-3 x-40 $$  
    Factorización: $$ (x-8)(x+5) $$

15. $$ x^{2}-15 x+56 $$  
    Factorización: $$ (x-8)(x-7) $$

16. $$ 3 x^{2}+10 x+7 $$  
    Factorización: $$ (x+1)(3x+7) $$

17. $$ 5 x^{2}-17 x+6 $$  
    Factorización: $$ (x-3)(5x-2) $$

18. $$ 18 x^{2}-33 x+14 $$  
    Factorización: $$ (3x-2)(6x-7) $$

Si necesitas más ayuda o detalles sobre alguna de las factorizaciones, no dudes en preguntar.
Aquí están las factorizaciones de las expresiones: 6. $$ 121 a^{6}-144 b^{a} $$ No se pudo factorizar. 7. $$ x^{3}-27 $$ $$ (x-3)(x^{2}+3x+9) $$ 8. $$ 8 y^{3}+125 $$ $$ (2y+5)(4y^{2}-10y+25) $$ 9. $$ 216 a^{9}-343 b^{6} $$ $$ (6a^{3}-7b^{2})(36a^{6}+42a^{3}b^{2}+49b^{4}) $$ 10. $$ x^{2}-10 x+25 $$ $$ (x-5)^{2} $$ 11. $$ 36 y^{2}+60 y+25 $$ $$ (6y+5)^{2} $$ 12. $$ 81 a^{4}-108 a^{2} b+36 b^{2} $$ $$ 9(3a^{2}-2b)^{2} $$ 13. $$ x^{2}+9 x+20 $$ $$ (x+4)(x+5) $$ 14. $$ x^{2}-3 x-40 $$ $$ (x-8)(x+5) $$ 15. $$ x^{2}-15 x+56 $$ $$ (x-8)(x-7) $$ 16. $$ 3 x^{2}+10 x+7 $$ $$ (x+1)(3x+7) $$ 17. $$ 5 x^{2}-17 x+6 $$ $$ (x-3)(5x-2) $$ 18. $$ 18 x^{2}-33 x+14 $$ $$ (3x-2)(6x-7) $$ Si necesitas más ayuda con alguna de estas factorizaciones, no dudes en preguntar.

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