Recognize as difference of squares: Recognize the expression as a difference of squares.The given expression is in the form of a2−b2, which is a difference of squares.a2−b2 can be factored into (a+b)(a−b).Here, a=(9x+7) and b=(x+1).
Apply formula: Apply the difference of squares formula.Using the formula from Step 1, we can write the expression as:((9x+7)+(x+1))((9x+7)−(x+1))
Simplify each factor: Simplify each factor.First factor: (9x+7)+(x+1)=9x+7+x+1=10x+8Second factor: (9x+7)−(x+1)=9x+7−x−1=8x+6
Check for common factors: Check for common factors in the simplified terms.Both 10x+8 and 8x+6 have common factors.10x+8 can be divided by 2 to get 5x+4.8x+6 can be divided by 2 to get 4x+3.
Write final factored form: Write the final factored form.The complete factorization of the expression is:(2(5x+4))(2(4x+3))
Multiply common factors: Multiply the common factors outside the parentheses.The final factored form is:2×2×(5x+4)(4x+3)=4(5x+4)(4x+3)