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Consider the following special types of polynomials.

difference of squares, perfect square, sum or difference of cubes in order to answer the question for each case

Which of the special types of polynomial models would you use to easily factor the following expressions? Explain and complete factor them.

1) 16y^2+ 24y + 9

2) 49x^2 – 100y^2

3) 27x^3 + 64y^3

4) x^3 - 125

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1 Answer

1) use perfect square formula a2+2ab+b2=(a+b)2

16y2 + 24y + 9 = (4y)2 + 2.4y.3 + 32 = (4y+3)2

2) use difference of squares formula a2 - b2 = (a+b)(a-b)

49x2 - 100y2 = (7x)2 - (10y)2 = (7x-10y)(7x+10y)

3) use sum of cubes formula, a3 + b3 = (a+b)(a2-ab+b2)

27x3 + 64y3 = (3x)3 + (4y)3 = (3x+4y)(9x2-12xy+16y2)

4) use difference of cubes formula, a3 - b3 = (a-b)(a2+ab+b2)

x3 - 125 = x3 - 53 = (x-5)(x2+5x+25)