Factorize completely,

  1. (i)

    x2y4−z6x^{2}y^{4} - z^{6}

    Answer ___

  2. (ii)

    15a^{2} - 6a + 20ab - 8b

    Answer ___

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Worked solution

8(i)

1. Rewrite each term as a square

x2y4−z6=(xy2)2−(z3)2x^2y^4-z^6=(xy^2)^2-(z^3)^2

2. Apply the difference of squares identity

(xy2)2−(z3)2=(xy2+z3)(xy2−z3)(xy^2)^2-(z^3)^2=(xy^2+z^3)(xy^2-z^3)

Answer

(xy2+z3)(xy2−z3)(xy^2+z^3)(xy^2-z^3)

8(ii)

1. Group terms and factorise each pair

15a2−6a+20ab−8b=3a(5a−2)+4b(5a−2)15a^2-6a+20ab-8b=3a(5a-2)+4b(5a-2)

2. Factor out the common binomial

3a(5a−2)+4b(5a−2)=(3a+4b)(5a−2)3a(5a-2)+4b(5a-2)=(3a+4b)(5a-2)

Answer

(3a+4b)(5a−2)(3a+4b)(5a-2)

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