a) $$ (8 x+5)(9 x-12)= $$ b) $$ (7 x-4)\left(8 x^{2}+9 x\right)= $$ c) $$ 8 x^{4}\left(9 x^{2}+6 x^{3}-12 x^{4}\right)= $$ d) $$ \left(\frac{2}{7} x^{3}\right)\left(\frac{3}{5} x^{5}\right)= $$ e) $$ \left(2 x^{3} y+x^{2} y^{2}\right)\left(7 x^{2} y-2 x y\right)= $$

Question

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(7x-4ight)\left(8x^{2}+9xight)$$
- step1: Apply the distributive property:
  $$7x	imes 8x^{2}+7x	imes 9x-4	imes 8x^{2}-4	imes 9x$$
- step2: Multiply the terms:
  $$56x^{3}+63x^{2}-32x^{2}-36x$$
- step3: Subtract the terms:
  $$56x^{3}+31x^{2}-36x$$
Expand the expression $$ 8 x^{4}(9 x^{2}+6 x^{3}-12 x^{4}) $$
Simplify the expression by following steps:
- step0: Simplify:
  $$8x^{4}\left(9x^{2}+6x^{3}-12x^{4}ight)$$
- step1: Rewrite the expression:
  $$8\left(9x^{2}+6x^{3}-12x^{4}ight)x^{4}$$
- step2: Multiply the expression:
  $$24\left(3+2x-4x^{2}ight)x^{6}$$
- step3: Rearrange the terms:
  $$72x^{6}+48x^{7}-96x^{8}$$
Expand the expression $$ \left(2 x^{3} y+x^{2} y^{2}ight)\left(7 x^{2} y-2 x yight) $$
Simplify the expression by following steps:
- step0: Simplify:
  $$\left(2x^{3}y+x^{2}y^{2}ight)\left(7x^{2}y-2xyight)$$
- step1: Multiply the expression:
  $$\left(14x^{2}-4x+7yx-2yight)y^{2}x^{3}$$
- step2: Rearrange the terms:
  $$14x^{5}y^{2}-4x^{4}y^{2}+7y^{3}x^{4}-2y^{3}x^{3}$$
Expand the expression $$ (8 x+5)(9 x-12) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(8x+5ight)\left(9x-12ight)$$
- step1: Apply the distributive property:
  $$8x	imes 9x-8x	imes 12+5	imes 9x-5	imes 12$$
- step2: Multiply the terms:
  $$72x^{2}-96x+45x-60$$
- step3: Add the terms:
  $$72x^{2}-51x-60$$
Expand the expression $$ \left(\frac{2}{7} x^{3}ight)\left(\frac{3}{5} x^{5}ight) $$
Simplify the expression by following steps:
- step0: Simplify:
  $$\left(\frac{2}{7}x^{3}ight)\left(\frac{3}{5}x^{5}ight)$$
- step1: Multiply the terms:
  $$\frac{2}{7}x^{3}\left(\frac{3}{5}x^{5}ight)$$
- step2: Multiply the terms:
  $$\frac{2}{7}x^{3}	imes \frac{3}{5}x^{5}$$
- step3: Multiply the numbers:
  $$\frac{6}{35}x^{3}	imes x^{5}$$
- step4: Multiply the terms:
  $$\frac{6}{35}x^{8}$$
Aquí están las soluciones a cada uno de los problemas:

a) $$ (8 x+5)(9 x-12) = 72x^{2}-51x-60 $$

b) $$ (7 x-4)(8 x^{2}+9 x) = 56x^{3}+31x^{2}-36x $$

c) $$ 8 x^{4}(9 x^{2}+6 x^{3}-12 x^{4}) = 72x^{6}+48x^{7}-96x^{8} $$

d) $$ \left(\frac{2}{7} x^{3}ight)\left(\frac{3}{5} x^{5}ight) = \frac{6}{35}x^{8} $$

e) $$ \left(2 x^{3} y+x^{2} y^{2}ight)\left(7 x^{2} y-2 x yight) = 14x^{5}y^{2}-4x^{4}y^{2}+7y^{3}x^{4}-2y^{3}x^{3} $$

Si necesitas más ayuda o explicaciones sobre algún paso, no dudes en preguntar.
a) $$ (8x + 5)(9x - 12) = 72x^2 - 51x - 60 $$ b) $$ (7x - 4)(8x^2 + 9x) = 56x^3 + 31x^2 - 36x $$ c) $$ 8x^4(9x^2 + 6x^3 - 12x^4) = 72x^6 + 48x^7 - 96x^8 $$ d) $$ \left(\frac{2}{7}x^3ight)\left(\frac{3}{5}x^5ight) = \frac{6}{35}x^8 $$ e) $$ \left(2x^3y + x^2y^2ight)\left(7x^2y - 2xyight) = 14x^5y^2 - 4x^4y^2 + 7x^4y^3 - 2x^3y^3 $$

a) \( (8 x+5)(9 x-12)= \) b) \( (7 x-4)\left(8 x^{2}+9 x\right)= \) c) \( 8 x^{4}\left(9 x^{2}+6 x^{3}-12 x^{4}\right)= \) d) \( \left(\frac{2}{7} x^{3}\right)\left(\frac{3}{5} x^{5}\right)= \) e) \( \left(2 x^{3} y+x^{2} y^{2}\right)\left(7 x^{2} y-2 x y\right)= \)

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