Question

simplify:- (3√5-5√2)(4√5+3√2)​

Answer 1

Answer:

HEY MATE HERE IS YOUR ANSWER

Answer 2

Answer:

$\left(3\sqrt{5}-5\sqrt{2}\right)\left(4\sqrt{5}+3\sqrt{2}\right)=30-11\sqrt{10}\quad \left(\mathrm{Decimal:\quad }\:-4.78505\dots \right)$

Step-by-step explanation:

$\left(3\sqrt{5}-5\sqrt{2}\right)\left(4\sqrt{5}+3\sqrt{2}\right)$

$\gray{\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd}$

$\gray{a=3\sqrt{5},\:b=-5\sqrt{2},\:c=4\sqrt{5},\:d=3\sqrt{2}}$

$=3\sqrt{5}\cdot \:4\sqrt{5}+3\sqrt{5}\cdot \:3\sqrt{2}+\left(-5\sqrt{2}\right)\cdot \:4\sqrt{5}+\left(-5\sqrt{2}\right)\cdot \:3\sqrt{2}$

$\gray{\mathrm{Apply\:minus-plus\:rules}}$

$\gray{+\left(-a\right)=-a}$

$=3\cdot \:4\sqrt{5}\sqrt{5}+3\cdot \:3\sqrt{5}\sqrt{2}-5\cdot \:4\sqrt{2}\sqrt{5}-5\cdot \:3\sqrt{2}\sqrt{2}$

$\black{\mathrm{Simplify}\:3\cdot \:4\sqrt{5}\sqrt{5}+3\cdot \:3\sqrt{5}\sqrt{2}-5\cdot \:4\sqrt{2}\sqrt{5}-5\cdot \:3\sqrt{2}\sqrt{2}:}$

$3\cdot \:4\sqrt{5}\sqrt{5}+3\cdot \:3\sqrt{5}\sqrt{2}-5\cdot \:4\sqrt{2}\sqrt{5}-5\cdot \:3\sqrt{2}\sqrt{2}$

$\gray{3\cdot \:4\sqrt{5}\sqrt{5}=60}$

$\gray{3\cdot \:3\sqrt{5}\sqrt{2}=9\sqrt{10}}$

$\gray{5\cdot \:4\sqrt{2}\sqrt{5}=20\sqrt{10}}$

$\gray{5\cdot \:3\sqrt{2}\sqrt{2}=30}$

$=60+9\sqrt{10}-20\sqrt{10}-30$

$\gray{\mathrm{Add\:similar\:elements:}\:9\sqrt{10}-20\sqrt{10}=-11\sqrt{10}}$

$=60-11\sqrt{10}-30$$\left(3\sqrt{5}-5\sqrt{2}\right)\left(4\sqrt{5}+3\sqrt{2}\right)$

$\gray{\mathrm{Subtract\:the\:numbers:}\:60-30=30}$

$=30-11\sqrt{10}$