Fill in the blanks. (i) x2 - 18 x + 81 = (…) (ii) 4 - 36x2 = (…)

1.	Fill in the blanks. (i) x2 - 18 x + 81 = (…) (ii) 4 - 36x2 = (…)(...) (iii) x2 - 14x + 13 = (…)(…) (iv) 9z2 - x2 - 4y2 + 4xy = (…)(…) (v) abc - ab - c + 1 = (…)(…)
Answer» Using the identity : a² – b² = (a + b)(a-b) (i) x² - 18x + 81 = x² - (9x) + 81 = (x - 9)(x - 9) = (x - 9)² (ii) (4 - 36 x²) = 4(1 - 9x²) = 4(1 - 3x)(1 + 3x) (iii) x² - 14x + 13 = x²–(13 + 1)x + 13 = x(x - 13) - 1(x - 13) = (x - 13)(x - 1) (iv) 9z² - x² - 4y² + 4xy = 9z² - (x - 2y)² = (3z - x + 2y)(3z + x - 2y) (v) abc - ab - c + 1 = ab(c - 1) - (c - 1) = (ab - 1)(c - 1)

Fill in the blanks. (i) x2 - 18 x + 81 = (…) (ii) 4 - 36x2 = (…)(...) (iii) x2 - 14x + 13 = (…)(…) (iv) 9z2 - x2 - 4y2 + 4xy = (…)(…) (v) abc - ab - c + 1 = (…)(…)

Answer»

Using the identity : a² – b² = (a + b)(a-b)

(i) x² - 18x + 81 = x² - (9x) + 81 = (x - 9)(x - 9) = (x - 9)²

(ii) (4 - 36 x²) = 4(1 - 9x²) = 4(1 - 3x)(1 + 3x)

(iii) x² - 14x + 13 = x²–(13 + 1)x + 13 = x(x - 13) - 1(x - 13) = (x - 13)(x - 1)

(iv) 9z² - x² - 4y² + 4xy = 9z² - (x - 2y)² = (3z - x + 2y)(3z + x - 2y)

(v) abc - ab - c + 1 = ab(c - 1) - (c - 1) = (ab - 1)(c - 1)

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Fill in the blanks. (i) x2 - 18 x + 81 = (…) (ii) 4 - 36x2 = (…)(...) (iii) x2 - 14x + 13 = (…)(…) (iv) 9z2 - x2 - 4y2 + 4xy = (…)(…) (v) abc - ab - c + 1 = (…)(…)
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