Question

A(a-1)(a+1)-(a-2)(a^2+2a+4)=

Answer 1

$a(a - 1)(a + 1) - (a - 2)(a {}^{2} + 2a + 4) = a(a {}^{2} - 1) - (a {}^{3} - 8) = a {}^{3} - a - a {}^{3} + 8 = 8 - a$

Answer 2

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Answer 3

Let's simplify the expression step by step:

A(a-1)(a+1) - (a-2)(a^2 + 2a + 4)

Step 1: Expand the expressions within the parentheses:

A(a^2 + a - a - 1) - (a^3 + 2a^2 + 4a - 2)

Step 2: Combine like terms within each expression:

A(a^2 - 1) - (a^3 + 2a^2 + 4a - 2)

Step 3: Distribute A to the terms inside the first parentheses:

A * a^2 - A * 1 - (a^3 + 2a^2 + 4a - 2)

Step 4: Simplify further:

A * a^2 - A - a^3 - 2a^2 - 4a + 2

Step 5: Combine like terms:

(A * a^2 - 2a^2) - A - a^3 - 4a + 2

Step 6: Factor out common terms in the first parentheses:

a^2 (A - 2) - A - a^3 - 4a + 2

So, the simplified expression is: a^2(A - 2) - A - a^3 - 4a + 2