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( a+ b) ( a- b) ( a square + 4 square )​

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Answer:

[tex]\sf a^4 +16a^2 -b^2 a^2 -16b^2[/tex]

Explanation:

[tex]\sf ( a+ b) ( a- b) ( a^2 + 4^2)[/tex]

expand

[tex]\sf (a^2-ba+ba-b^2 ) ( a^2 + 16)[/tex]

simplify

[tex]\sf (a^2-b^2 ) ( a^2 + 16)[/tex]

expand

[tex]\sf a^4 +16a^2 -b^2 a^2 -16b^2[/tex]

Solution:

Note that:

  • Given expression: (a + b)(a - b)(a² + 4²)

Formula: (a + b)(a - b) = a² - b²

Simplify the expression using the formula.

  • (a + b)(a - b)(a² + 4²)
  • => {(a + b)(a - b)}(a² + 4²)
  • => (a² - b²)(a² + 16)
  • => a⁴ + 16a² - a²b² - 16b²
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