1)x^4(8x-1)^2 =x^4(64x^2-16x+1) =64x^6-16x^5+x^4
2)(8x^3-x^2)^2 =64x^6-16x^5+x^4
3)x^4(8x-1)(8x+1) =x^4(64x^2-1) =64x^6-x^4
4)x^4(64x^2-1) =64x^6-x^4
64 x 6 − x 4 = x 4 ( 64 x 2 − 1 ) = x 4 [ ( 8 x ) 2 − 1 2 ] = x 4 ( 8 x − 1 ) ( 8 x + 1 ) a 2 − b 2 = ( a − b ) ( a + b )
To factor the expression 63x^5 - 70x^3 + 15x completely, we first factor out x, then apply the quadratic factorization approach. We find the roots to arrive at the final factored form of x(3(21x^2 - 5))(x - 1)(x + 1). This method ensures we break down the polynomial into its simplest form by utilizing common factors and restructuring quadratic terms.
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