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) \( \left(2 x^{3} y+x^{2} y^{2}\right)\left(7 x^{2} y-2 x y\right)= \)

Simplify the expression by following steps: - step0: Multiply the terms: \(\left(7x-4\right)\left(8x^{2}+9x\right)\) - step1: Apply the distributive property: \(7x\times 8x^{2}+7x\times 9x-4\times 8x^{2}-4\times 9x\) - 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: \(8x^{4}\left(9x^{2}+6x^{3}-12x^{4}\right)\) - step1: Rewrite the expression: \(8\left(9x^{2}+6x^{3}-12x^{4}\right)x^{4}\) - step2: Multiply the expression: \(24\left(3+2x-4x^{2}\right)x^{6}\) - step3: Rearrange the terms: \(72x^{6}+48x^{7}-96x^{8}\) Expand the expression \( \left(2 x^{3} y+x^{2} y^{2}\right)\left(7 x^{2} y-2 x y\right) \) Simplify the expression by following steps: - step0: Simplify: \(\left(2x^{3}y+x^{2}y^{2}\right)\left(7x^{2}y-2xy\right)\) - step1: Multiply the expression: \(\left(14x^{2}-4x+7yx-2y\right)y^{2}x^{3}\) - 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: \(\left(8x+5\right)\left(9x-12\right)\) - step1: Apply the distributive property: \(8x\times 9x-8x\times 12+5\times 9x-5\times 12\) - step2: Multiply the terms: \(72x^{2}-96x+45x-60\) - step3: Add the terms: \(72x^{2}-51x-60\) Expand the expression \( \left(\frac{2}{7} x^{3}\right)\left(\frac{3}{5} x^{5}\right) \) Simplify the expression by following steps: - step0: Simplify: \(\left(\frac{2}{7}x^{3}\right)\left(\frac{3}{5}x^{5}\right)\) - step1: Multiply the terms: \(\frac{2}{7}x^{3}\left(\frac{3}{5}x^{5}\right)\) - step2: Multiply the terms: \(\frac{2}{7}x^{3}\times \frac{3}{5}x^{5}\) - step3: Multiply the numbers: \(\frac{6}{35}x^{3}\times x^{5}\) - 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) \( \left(\frac{2}{7} x^{3}\right)\left(\frac{3}{5} x^{5}\right) = \frac{6}{35}x^{8} \) e) \( \left(2 x^{3} y+x^{2} y^{2}\right)\left(7 x^{2} y-2 x y\right) = 14x^{5}y^{2}-4x^{4}y^{2}+7y^{3}x^{4}-2y^{3}x^{3} \) Si necesitas más ayuda o explicaciones sobre algún paso, no dudes en preguntar.