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103 × 107 103 × 107 = (100 + 3) × (100 + 7) = (100) 2 + (3 + 7) (100 + (3)(7)) | Using Identity IV = 10000 + 1000 + 21 = 11021. Aliter 103 × 107 = (105 - 2) × (105 + 2) = (105) 2 - (2) 2 | Using Identity III = (100 + 5) 2 - 4 = (100) 2 + 2(100)(5) + (5) 2 - 4 | Using Identity I = 10000 + 1000 + 25 - 4 = 11021.

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Polynomials

Short Answer Type

141. Check whether (p + 1) is a factor of (p¹⁰⁰ - 1) and (p¹⁰⁰ - 1).

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142. Factorise: 3u³ + 4u² - 12u + 16.

222 Views

143. Find if remainder obtained on dividing polynomial p(y) = y³ + ay² + 5y - 25 by (y + a) is a factor of polynomial f(a) = a² -5a + 25.

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144. If (2x - 3) is a factor of 2x⁴ - 3x² + 15x - 15k, find the value of

open parentheses 3 straight k minus square root of 5 space straight k close parentheses.

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145.

Use suitable identities to find the following products:

(i) (x + 4)(x + 10)

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146.

Use suitable identities to find the following products:

(x + 8)(x - 10)

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147.

Use suitable identities to find the following products:

(3x + 4)(3x - 5)

359 Views

148.

Use suitable identities to find the following products:

$open parentheses straight y squared plus 3 over 2 close parentheses open parentheses y squared minus 3 over 2 close parentheses$

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149.

Use suitable identities to find the following products:
(3 - 2x)(3 + 2x)

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150. Evaluate the following products without multiplying directly:
103 × 107

103 × 107
103 × 107 = (100 + 3) × (100 + 7)
= (100)² + (3 + 7) (100 + (3)(7))
| Using Identity IV
= 10000 + 1000 + 21 = 11021.
Aliter
103 × 107 = (105 - 2) × (105 + 2)
= (105)² - (2)²| Using Identity III
= (100 + 5)² - 4
= (100)² + 2(100)(5) + (5)² - 4
| Using Identity I
= 10000 + 1000 + 25 - 4 = 11021.