Multiply the monomial by the binomial and find the value of each for x = −1, y = 0.25 and z = 0.05:
(i) 15y²(2 − 3x)
(ii) −3x(y² + z²)
(iii) z²(x − y)
(iv) xz(x² + y²)

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Solution

(i) To find the product, we will use distributive law as follows:

$15 y^{2} (2 - 3 x) = 15 y^{2} \times 2 - 15 y^{2} \times 3 x = 30 y^{2} - 45 x y^{2}$

Substituting x = $-$ 1 and y = 0.25 in the result, we get:

$30 y^{2} - 45 x y^{2} = 30 {(0.25)}^{2} - 45 (- 1) {(0.25)}^{2} = 30 \times 0.0625 - \{45 \times (- 1) \times 0.0625\} = 30 \times 0.0625 - \{45 \times (- 1) \times 0.0625\} = 1.875 - (- 2.8125) = 1.875 + 2.8125 = 4.6875$

(ii) To find the product, we will use distributive law as follows:

$- 3 x (y^{2} + z^{2}) = - 3 x \times y^{2} + (- 3 x) \times z^{2} = - 3 x y^{2} - 3 x z^{2}$

Substituting x = $-$ 1, y = 0.25 and z = 0.05 in the result, we get:

$- 3 x y^{2} - 3 x z^{2} = - 3 (- 1) {(0.25)}^{2} - 3 (- 1) {(0.05)}^{2} = - 3 (- 1) (0.0625) - 3 (- 1) (0.0025) = 01875 + 0.0075 = 0.195$

(iii) To find the product, we will use distributive law as follows:

$z^{2} (x - y) = z^{2} \times x - z^{2} \times y = x z^{2} - y z^{2}$

Substituting x = $-$ 1, y = 0.25 and z = 0.05 in the result, we get:

$x z^{2} - y z^{2} = (- 1) {(0.05)}^{2} - (0.25) {(0.05)}^{2} = (- 1) (0.0025) - (0.25) (0.0025) = - 0.0025 - 0.000625 = - 0.003125$

(iv) To find the product, we will use distributive law as follows:

$x z (x^{2} + y^{2}) = x z \times x^{2} + x z \times y^{2} = x^{3} z + x y^{2} z$

Substituting x = $-$ 1, y = 0.25 and z = 0.05 in the result, we get:

$x^{3} z + x y^{2} z = {(- 1)}^{3} (0.05) + (- 1) {(0.25)}^{2} (0.05) = (- 1) (0.05) + (- 1) (0.0625) (0.05) = - 0.05 - 0.003125 = - 0.053125$

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