Question

simplify (3+2√2)(3-2√2)​

Answer 1

Answer:

1

Step-by-step explanation:

first multiply 3 with 3-2√2

then multiply 2√2 with 3-2√2

then cancel+-

Answer 2

Answer:

$\left(3+2\sqrt{2}\right)\left(3-2\sqrt{2}\right)=1$

Step-by-step explanation:

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

$\gray{\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}\left(a+b\right)\left(a-b\right)=a^2-b^2}$

$\gray{a=3,\:b=2\sqrt{2}}$

$=3^2-\left(2\sqrt{2}\right)^2$

$\black{\mathrm{Simplify}\:3^2-\left(2\sqrt{2}\right)^2:}$

$3^2-\left(2\sqrt{2}\right)^2$

$\black{3^2=9}$

$\black{\left(2\sqrt{2}\right)^2}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n}$

$=2^2\left(\sqrt{2}\right)^2$

$\gray{\left(\sqrt{2}\right)^2:\quad 2}$

$=2^2\cdot \:2$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}}$

$\gray{2^2\cdot \:2=\:2^{2+1}}$

$=2^{2+1}$

$\gray{\mathrm{Add\:the\:numbers:}\:2+1=3}$

$=2^3$

$\gray{2^3=8}$

$=8$

$=9-8$

$\gray{\mathrm{Subtract\:the\:numbers:}\:9-8=1}$

$=1$