Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Factorising two term cubic expressions.
Test Yourself 1 - Solutions.

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Both terms monic.	1. a3 - b3 = (a)3- (b)3 = (a - b)(a2 + ab + b2)	2. c3 + d3 = (c)3 + (d)3 = (c + d)(c2 - cd + d2)
	3. 5f3 + 5g3 = 5[(f)3 + (g)3] = 5(f + g)(f2 - fg + g2)	4. (x - h)3 - x3 = (x - h)3 - (x)3 = (x - h - x)((x-h)2 - (x - h)d + d2) = -h((x-h)2 - (x - h)d + d2)
	5. (x - 1)3 + (y + 1)3 = (x - 1 + y + 1)((x - 1)2 - (x - 1)(y + 1) + (y + 1)2) = (x + y)((x - 1)2 - (x - 1)(y + 1) + (y + 1)2)
	6. x6 - 1 = (x2)3 - (1)3 = (x2 - 1)(x4 + x2 + 1) = (x + 1)(x - 1)(x4 + x2 + 1)
First term monic.	7. m3 + 8n3 = (m)3 + (2n)3 = (m + 2n)(m2 - 2mn + 4n2)	8. x3 - 216y3 = (x)3 - (6y)3 = (x - 6y)(x2 + 6xy + 36y2)
	9. 2p3 - 54q3 = 2(p3 - 27q3) = 2((p)3 - (3q)3) = 2((p - 3q)(p2 + 3pq + 9q2)	10. r3 + 125s3 = (r)3 + (5s)3 = (r + 5s)(r2 - 5sr + 24s2)
	11.	12.
Second term monic.	13. 27m3 - b3 = (3m)3 - (b)3 = (3m - b)(9m2 + 3mb + b2)	14. 24m3 + 3n3 = 3(8m3 + n3) = 3((2m)3 + (n)3) =3(2m + n)(4m2 - 2mn + n2)
	15. 53x - 1 = (5x)3 - (1)3 = (5x - 1)(25x2 + 5x + 1)	16. 40p3 + 5q3 = 5(8p3 + q3) = 5((2p)3 + (q)3) = 5(2p + q)(4p2 + 3pq + q2)
	17. 8 + (m + 1)3 = (2)3 + (m + 1)3 = (2 + m + 1)(22 - 2(m + 1) + (m + 1)2) = (3 + m)(2 - 2m + (m + 1)2) = (3 + m)(3 + m2)	18.
Neither term monic.	19. 8d3 - 27y3 = (2d)3 - (3y)3 = (2d - 3y)(4d2 + 6dy + 9y2)	20. 27 + (x - 3)3 = 33 + (x - 3)3 = (3 + x - 3)(9 - 3(x - 3) + (x - 3)2) = x(x2 - 9x + 27)
	21. 8(x - y)3 + 27(x + y)3 = (2(x - y))3 +(3(x + y))3 = (2x - 2y + 3x +3y)(4x2 - 8xy + 4y2 + 6x2 - 6y2 + 9x2 + 18xy + 9y2) = (5x + y)(19x2 + 10xy + 7y2)	22.
	23. 8a6b3 + 64c3d6 = 8((a2b)3 + (2cd2)3) = 8(a2b + 2cd2)(a4b2 - 2a2bcd2 + 4c2d4)	24.