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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

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179.
Simplify:

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

open parentheses straight x minus 2 over 3 straight y close parentheses cubed minus open parentheses straight x plus 2 over 3 straight y close parentheses cubed equals space open square brackets straight x cubed minus open parentheses 2 over 3 straight y close parentheses cubed minus 3 left parenthesis straight x right parenthesis open parentheses 2 over 3 straight y close parentheses open curly brackets open parentheses straight x close parentheses minus open parentheses 2 over 3 straight y close parentheses close curly brackets close square brackets equals space open square brackets straight x cubed minus open parentheses 2 over 3 straight y close parentheses cubed plus 3 left parenthesis straight x right parenthesis open parentheses 2 over 3 straight y close parentheses open curly brackets open parentheses straight x close parentheses plus open parentheses 2 over 3 straight y close parentheses close curly brackets close square brackets equals open square brackets straight x cubed minus 8 over 27 straight y cubed minus 2 straight x squared straight y plus 4 over 3 xy squared close square brackets minus open square brackets straight x cubed plus 8 over 27 straight y cubed plus 2 straight x squared straight y plus 4 over 3 xy squared close square brackets equals space minus 16 over 27 straight y cubed minus 4 straight x squared straight y

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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

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Test Yourself

Short Answer Type

179. Simplify:

179.
Simplify:

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