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Factor completely:

(9x+7)^(2)-(x+1)^(2)
Answer:

Factor completely:\newline(9x+7)2(x+1)2 (9 x+7)^{2}-(x+1)^{2} \newlineAnswer:

Full solution

Q. Factor completely:\newline(9x+7)2(x+1)2 (9 x+7)^{2}-(x+1)^{2} \newlineAnswer:
  1. Recognize as difference of squares: Recognize the expression as a difference of squares.\newlineThe given expression is in the form of a2b2a^2 - b^2, which is a difference of squares.\newlinea2b2a^2 - b^2 can be factored into (a+b)(ab)(a + b)(a - b).\newlineHere, a=(9x+7)a = (9x + 7) and b=(x+1)b = (x + 1).
  2. Apply formula: Apply the difference of squares formula.\newlineUsing the formula from Step 11, we can write the expression as:\newline((9x+7)+(x+1))((9x+7)(x+1)) ((9x + 7) + (x + 1))((9x + 7) - (x + 1))
  3. Simplify each factor: Simplify each factor.\newlineFirst factor: (9x+7)+(x+1)=9x+7+x+1=10x+8(9x + 7) + (x + 1) = 9x + 7 + x + 1 = 10x + 8\newlineSecond factor: (9x+7)(x+1)=9x+7x1=8x+6(9x + 7) - (x + 1) = 9x + 7 - x - 1 = 8x + 6
  4. Check for common factors: Check for common factors in the simplified terms.\newlineBoth 10x+810x + 8 and 8x+68x + 6 have common factors.\newline10x+810x + 8 can be divided by 22 to get 5x+45x + 4.\newline8x+68x + 6 can be divided by 22 to get 4x+34x + 3.
  5. Write final factored form: Write the final factored form.\newlineThe complete factorization of the expression is:\newline(2(5x+4))(2(4x+3))(2(5x + 4))(2(4x + 3))
  6. Multiply common factors: Multiply the common factors outside the parentheses.\newlineThe final factored form is:\newline2×2×(5x+4)(4x+3)2 \times 2 \times (5x + 4)(4x + 3)\newline=4(5x+4)(4x+3)= 4(5x + 4)(4x + 3)

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