We read your photo as:

Factorize the expression (x2 - 9)2 + 16(x2 - 9) + 64.

Mathematics

ScanSolve AI Answer

Answer

(x−1)2(x+1)2(x-1)^2 (x+1)^2

Step-by-step solution

8 steps

  1. Identify the given expression.

    The expression to factorize is (x2−9)2+16(x2−9)+64(x^2 - 9)^2 + 16(x^2 - 9) + 64.

  2. Use substitution to simplify the expression.

    Let y=x2−9y = x^2 - 9. Substitute yy into the expression:

    y2+16y+64y^2 + 16y + 64

  3. Factor the quadratic expression in terms of yy.

    This is a perfect square trinomial of the form a2+2ab+b2=(a+b)2a^2 + 2ab + b^2 = (a+b)^2.
    Here, a=ya=y and b=8b=8, since 2(y)(8)=16y2(y)(8) = 16y and 82=648^2 = 64.
    So, the expression factors to:

    (y+8)2(y+8)^2

  4. Substitute back x2−9x^2 - 9 for yy.

    ((x2−9)+8)2((x^2 - 9) + 8)^2

  5. Simplify the expression inside the parenthesis.

    (x2−9+8)2=(x2−1)2(x^2 - 9 + 8)^2 = (x^2 - 1)^2

  6. Factor the term inside the parenthesis using the difference of squares formula, a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b).

    Here, x2−1x^2 - 1 can be written as x2−12x^2 - 1^2.
    So, x2−1=(x−1)(x+1)x^2 - 1 = (x-1)(x+1).

  7. Substitute this factored form back into the expression.

    ((x−1)(x+1))2((x-1)(x+1))^2

  8. Apply the exponent to both factors.

    (x−1)2(x+1)2(x-1)^2 (x+1)^2

    The fully factored expression is (x−1)2(x+1)2(x-1)^2 (x+1)^2.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QFactorize the expression x2 - 9.QFactorize the following: 3x2 - 7x − 6, x2 - 64, 9x2 - 25QFactorize x squared minus 9QFactorise the following expressions: x2 - 9, x2 - 64, 9y2 - 81
Browse by topic:Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.