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Find the following products:(i) (3x2 – 4xy) (3x2 – 3xy)(ii) (x + 1/5) (x + 5)(iii) (z + 3/4) (z + 4/3)(iv) (x2 + 4) (x2 + 9)(v) (y2 + 12) (y2 + 6)(vi) (y2 + 5/7) (y2 – 14/5) |
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Answer» (i) (3x2 – 4xy) (3x2 – 3xy) = 3x2 (3x2 – 3xy) – 4xy (3x2 – 3xy) = 9x4 – 9x3y – 12x3y + 12x2y2 = 9x4 – 21x3y + 12x2y2 (ii) (x + 1/5) (x + 5) = x (x + 1/5) + 5 (x + 1/5) = x2 + x/5 + 5x + 1 = x2 + 26/5x + 1 (iii) (z + 3/4) (z + 4/3) = z (z + 4/3) + 3/4 (z + 4/3) = z2 + 4/3z + 3/4z + 12/12 = z2 + 4/3z + 3/4z + 1 = z2 + 25/12z + 1 (iv) (x2 + 4) (x2 + 9) = x2 (x2 + 9) + 4 (x2 + 9) = x4 + 9x2 + 4x2 + 36 = x4 + 13x2 + 36 (v) (y2 + 12) (y2 + 6) = y2 (y2 + 6) + 12 (y2 + 6) = y4 + 6y2 + 12y2 + 72 = y4 + 18y2 + 72 (vi) (y2 + 5/7) (y2 – 14/5) = y2 (y2 – 14/5) + 5/7 (y2 – 14/5) = y4 – 14/5y2 + 5/7y2 – 2 = y4 – 73/35y2 – 2 |
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