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Polynomials

Short Answer Type

171.

Factorise each of the following:

x² + 2ax - b² - 2ab

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172.

Factorise each of the following:

(x² + x)² + 4(x² + x) - 12

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173. Simplify:

fraction numerator 73 cross times 73 cross times bold 73 bold cross times bold 27 bold cross times bold 27 bold cross times bold 27 over denominator bold 73 bold cross times bold 73 bold minus bold 73 bold cross times bold 27 bold plus bold 27 bold cross times bold 27 end fraction

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174. Factorise:

7 square root of 2 straight x squared minus 10 straight x minus 4 square root of 2

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175. Factorise:

2 square root of 2 straight a cubed plus 8 straight b cubed minus 27 straight c cubed plus 18 square root of 2 space abc

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176.

If $straight x minus 1 over straight x equals 3 comma$ then find the value of $straight x cubed minus 1 over straight x cubed.$

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177. Factorise: a⁷ + ab⁶.

straight a to the power of 7 plus ab to the power of 6 equals space straight a left parenthesis straight a to the power of 6 plus straight b to the power of 6 right parenthesis equals space straight a left curly bracket left parenthesis straight a squared right parenthesis cubed plus left parenthesis straight b squared right parenthesis cubed right curly bracket equals space straight a left parenthesis straight a squared plus straight b squared right parenthesis space left curly bracket left parenthesis straight a squared right parenthesis squared plus left parenthesis straight b squared right parenthesis squared minus left parenthesis straight a squared right parenthesis left parenthesis straight b squared right parenthesis right curly bracket equals space straight a left parenthesis straight a squared plus straight b squared right parenthesis left parenthesis straight a to the power of 4 plus straight b to the power of 4 minus straight a squared straight b squared right parenthesis equals space straight a left parenthesis straight a squared plus straight b squared right parenthesis left parenthesis straight a to the power of 4 plus straight b to the power of 4 plus 2 straight a squared straight b squared space minus space 2 straight a squared straight b squared space minus straight a squared straight b squared right parenthesis equals straight a left parenthesis straight a squared plus straight b squared right parenthesis space left curly bracket left parenthesis straight a squared plus straight b squared right parenthesis squared minus left parenthesis square root of 3 ab right parenthesis squared right curly bracket equals space straight a left parenthesis straight a squared plus straight b squared right parenthesis left parenthesis straight a squared plus straight b squared minus square root of 3 space ab right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis straight a squared plus straight b squared plus square root of 3 space ab right parenthesis

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178. Prove that

fraction numerator 0.75 cross times 0.75 cross times 0.75 plus 0.25 cross times 0.25 cross times 0.25 over denominator 0.75 cross times 0.75 minus 0.75 cross times 0.25 plus 0.25 cross times 0.25 end fraction equals 1

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179.

Simplify:

$open parentheses straight x minus 2 over 3 straight y close parentheses cubed minus open parentheses x plus 2 over 3 y close parentheses cubed$

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180.

Factorise:

$straight x squared plus fraction numerator 1 over denominator straight x squared plus 2 end fraction minus 2 minus 2 straight x minus 2 over straight x$

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

177. Factorise: a7 + ab6.

177. Factorise: a⁷ + ab⁶.