College Algebra (10th Edition)

$(5x)(25x^2+15x+3)$
With $1=1^3$, the given expression is equivalent to: $=(5x+1)^3-1^3$ RECALL: The difference of two cubes $a^3-b^3$ can be factored using the formula: $a^3-b^3=(a-b)(a^2+ab+b^2)$ Factor the given difference of two cubes using the formula above with $a=5x+1$ and $b=1$ to obtain: $(5x+1)^3-1^3 \\=[(5x+1)-1][(5x+1)^2+(5x+1)(1)+1^2] \\=(5x+1-1)[(25x^2+2(5x)(1)+1^2)+(5x+1)+1] \\=(5x)[25x^2+10x+1+5x+1+1]$ Combine like terms to obtain: $=(5x)[25x^2+(10x+5x)+(1+1+1)] \\=(5x)(25x^2+15x+3)$