2. Factoniza las 5,9uientes expiesiones: a) $$ 14 a^{3} b^{5}+35 a^{2} b^{2}+49 a^{2} b+7 a^{2} b= $$ b) $$ x^{2}-15 x+56= $$ c) $$ 16 x^{4} y^{6}-25 x^{10} y^{8}= $$

Question

UpStudy AI · Accepted Answer

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 $$ 14 a^{3} b^{5}+35 a^{2} b^{2}+49 a^{2} b+7 a^{2} b $$.
Factor the expression by following steps:
- step0: Factor:
  $$14a^{3}b^{5}+35a^{2}b^{2}+49a^{2}b+7a^{2}b$$
- step1: Add the terms:
  $$14a^{3}b^{5}+35a^{2}b^{2}+56a^{2}b$$
- step2: Rewrite the expression:
  $$7a^{2}b	imes 2ab^{4}+7a^{2}b	imes 5b+7a^{2}b	imes 8$$
- step3: Factor the expression:
  $$7a^{2}b\left(2ab^{4}+5b+8ight)$$
Factor the expression $$ 16 x^{4} y^{6}-25 x^{10} y^{8} $$.
Factor the expression by following steps:
- step0: Factor:
  $$16x^{4}y^{6}-25x^{10}y^{8}$$
- step1: Factor the expression:
  $$x^{4}y^{6}\left(16-25x^{6}y^{2}ight)$$
- step2: Factor the expression:
  $$x^{4}y^{6}\left(4-5x^{3}yight)\left(4+5x^{3}yight)$$
Aquí están las factorizaciones de las expresiones dadas:

a) $$ 14 a^{3} b^{5}+35 a^{2} b^{2}+49 a^{2} b+7 a^{2} b = 7a^{2}b(2ab^{4}+5b+8) $$

b) $$ x^{2}-15 x+56 = (x-8)(x-7) $$

c) $$ 16 x^{4} y^{6}-25 x^{10} y^{8 = x^{4}y^{6}(4-5x^{3}y)(4+5x^{3}y) $$

Si necesitas más ayuda o aclaraciones, no dudes en preguntar.
a) $$ 14 a^{3} b^{5}+35 a^{2} b^{2}+49 a^{2} b+7 a^{2} b = 7a^{2}b(2ab^{4}+5b+8) $$ b) $$ x^{2}-15 x+56 = (x-8)(x-7) $$ c) $$ 16 x^{4} y^{6}-25 x^{10} y^{8} = x^{4}y^{6}(4-5x^{3}y)(4+5x^{3}y) $$

2. Factoniza las 5,9uientes expiesiones: a) \( 14 a^{3} b^{5}+35 a^{2} b^{2}+49 a^{2} b+7 a^{2} b= \) b) \( x^{2}-15 x+56= \) c) \( 16 x^{4} y^{6}-25 x^{10} y^{8}= \)

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