Question

Multiply and simplify: (10x2+7x+11)(2x2−5x+6)

Answer 1

Answer:

$=20x^4-36x^3+47x^2-13x+66$

Step-by-step explanation:

$\left(10x^2+7x+11\right)\left(2x^2-5x+6\right)\\=10x^2\cdot \:2x^2+10x^2\left(-5x\right)+10x^2\cdot \:6+7x\cdot \:2x^2+7x\left(-5x\right)+7x\cdot \:6+11\cdot \:2x^2+11\left(-5x\right)+11\cdot \:6\\\mathrm{Apply\:minus-plus\:rules}\\+\left(-a\right)=-a\\=10\cdot \:2x^2x^2-10\cdot \:5x^2x+10\cdot \:6x^2+7\cdot \:2x^2x-7\cdot \:5xx+7\cdot \:6x+11\cdot \:2x^2-11\cdot \:5x+11\cdot \:6\\=20x^4-50x^3+60x^2+14x^3-35x^2+42x+22x^2-55x+66\\=20x^4-50x^3+14x^3+60x^2-35x^2+22x^2+42x-55x+66$

$\mathrm{Add\:similar\:elements:}\:60x^2-35x^2+22x^2=47x^2\\=20x^4-50x^3+14x^3+47x^2+42x-55x+66\\\mathrm{Add\:similar\:elements:}\:-50x^3+14x^3=-36x^3\\=20x^4-36x^3+47x^2+42x-55x+66\\\mathrm{Add\:similar\:elements:}\:42x-55x=-13x\\=20x^4-36x^3+47x^2-13x+66$