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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.

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178. Prove that

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

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 space fraction numerator left parenthesis 0.75 right parenthesis cubed plus left parenthesis 0.25 right parenthesis cubed over denominator left parenthesis 0.75 right parenthesis squared plus left parenthesis 0.75 right parenthesis left parenthesis 0.25 right parenthesis plus left parenthesis 0.25 right parenthesis squared end fraction equals space fraction numerator left parenthesis 0.75 plus 0.25 right parenthesis left curly bracket left parenthesis 0.75 right parenthesis squared minus left parenthesis 0.75 right parenthesis left parenthesis 0.25 right parenthesis plus left parenthesis 0.25 right parenthesis squared right curly bracket over denominator left parenthesis 0.75 right parenthesis squared left parenthesis 0.75 right parenthesis left parenthesis 0.25 right parenthesis plus left parenthesis 0.25 right parenthesis squared end fraction equals space 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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