Exponentially Perfect PART 1

Algebra Level 1

( 2 3 2^{3} - 1 8 1^{8} )( 1 4 2 14^{2} - 1 3 2 13^{2} )


The answer is 189.

Francis Cabanting by Francis Cabanting , 21, Philippines

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1 solution

1 8 = 1 3 \color{#3D99F6}{1^8=1^3} .So the expression becomes ( 2 3 − 1 3 ) ( 1 4 2 − 1 3 2 ) \color{#20A900}{(2^3-1^3)(14^2-13^2)} .Using the factoring identities: { a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 ) a 2 − b 2 = ( a + b ) ( a − b ) \color{#D61F06}{\begin{cases}a^3-b^3=(a-b)(a^2+ab+b^2)\\a^2-b^2=(a+b)(a-b)\end{cases}} The expression becomes: ( 2 − 1 ) ( 2 2 + ( 2 ) ( 1 ) + 1 2 ) ( 14 + 13 ) ( 14 − 13 ) = 1 × 7 × 27 × 1 = 189 \color{#D61F06}{(2-1)(2^2+(2)(1)+1^2)(14+13)(14-13)\\=1\times7\times27\times1=\boxed{189}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

this can be simplified by taking 1^8=1

then, it comes down to 7 X 27 which is 189 \boxed {189 }

Yoogottam Khandelwal - 5 years, 11 months ago

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