POLQ 2 | Lesson 1 | Solutions (Factoring Trinomials)

Solutions:

Perfect Square Trinomials

\(x^2+10x+25 = (x+5)^2\) ;     \( r^2-8x+16 = (r-4)^2\)

\((4x)^2 -48x +36 = 4(2x-3)^2\)

Difference of Two Squares

\(121-y^2 = (11-y)(11+y)\)

\((x-2)^2-49 = ((x-2)-7)(x-2)+7)\) = (x – 9)(x+5)

Difference of Cubes

\(8x^3-27 = (2x-3)(4x^2 + 6x +9)\)

\(a^3 -125b^3= (a-5b)(a^2 +5ab +25b)\)

Sum of Cubes

\(x^3 +125 = (x+5)(x^2 – 5x +25)\)

\(m^3 + 8 = (m+2)(m^2 -2m +4)\)

\(2x^3 +128y^3 = 2(x^3 +64y^3)  = 2(x+4y)(x^2-4xy+16y)\)


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