Question

Factorize a^4-6a^2-7-8x-x^2

Answer 1

$a^{4}-6a^{2}-7-8x-x^{2} \\= (a^{2})^{2} - 2\times a^{2} \times 3 + 3^{2} - 3^{2} -7 -( x^{2} + 2\times x\times 4 + 4^{2} - 4^{2} ) \\= (a^{2})^{2} - 2\times a^{2} \times 3 + 3^{2} )- 9-7 -( x^{2} + 2\times x\times 4 + 4^{2}) + 16\\= (a^{2})^{2} - 2\times a^{2} \times 3 + 3^{2} )- 16 -( x^{2} + 2\times x\times 4 + 4^{2}) + 16\\= (a-3)^{2} - (x+4)^{2} \\= [(a-3)+(x+4)][(a-3)-(x+4)] \\= (a-3+x+4)(a-3-x-4)\\= (a+x+1)(a-x-7)$

Therefore.,

$\red {a^{4}-6a^{2}-7-8x-x^{2}}\green {= (a+x+1)(a-x-7) }$

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Answer 2

Answer:

(a^2+x+1) (a^2-x-7)