Question

Simiplify: $(7a-6b+5c{)}^2+(7a+6b-5c{)}^2$

Answer 1

Let us epxand the given expression:
$(7a-6b+5c{)}^2+(7a+6b-5c{)}^2=$
$\left[\right(7a{)}^2+(-6b{)}^2+(5c{)}^2+\{2\times (7a)\times (-6b\left)\right\}$$+\{2\times (-6b)\times 5c\}+\{2\times (7a)\times (5c\left)\right\}]$$+\left[\right(7a{)}^2+(6b{)}^2+(-5c{)}^2+\{2\times (7a)\times (6b\left)\right\}$$+\{2\times (6b)\times (-5c\left)\right\}+\{2\times (7a)\times (-5c\left)\right\}]$
by using the formula,
$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ac$
$=[49a^2+36b^2+25c^2+\{-84ab\}$$+\{-60bc\}+\left\{70ac\right\}+[49a^2+36b^2+25c^2+\{84ab\}$$+\{-60bc\}+\{-70ac\}]$
$=[49a^2+36b^2+25c^2-84ab-60bc+70ac]$$+[49a^2+36b^2+25c^2+84ab-60bc-70ac]$
$=[49a^2+36b^2+25c^2-84ab-60bc+70ac+49a^2$$+36b^2+25c^2+84ab-60bc-70ac$]
$=98a^2+72b^2+50c^2-120bc$
$\therefore (7a-6b+5c{)}^2+(7a+6b-5c{)}^2$$=98a^2+72b^2+50c^2-120bc$