Question

simplify the following by using algebraic identities class 8 (3a + 4b + 4c)² - (3a - 4b - 4c )²

Answer 1

We can use the identity a^2 - b^2 = (a+b)(a-b)
=> (3a + 4b + 4c + 3a -4b-4c)(3a+4b+4c-3a+4b+4c)
=> (6a) ( 8b + 8c)
=> 48ab + 48ac

Answer 2

8 (3a + 4b + 4c)² - (3a - 4b - 4c )²

[ (a+b+c)² = a²+b²+c²+2ab+2bc+2ca ]

= 8(9a²+16b²+16c²+24ab+32bc+24ac) -(9a²+16b²+16c²-24ab+32bc-24ca)

= 72a²+128b²+128c²+192ab+256bc+192ac-9a²-16b²-16c²+24ab-32bc+24ac

= 72a²-9a²+128b²-16b²+128c²-16c²+192ab+24ab+256bc-32bc+192ac+24ac

= 63a²+112b²+112c²+216ab+224bc+116ac