What is factor 49(y-4)^2-9(y+2)^2 ?

The solution to factor 49(y-4)^2-9(y+2)^2 is 4(5y-11)(2y-17)

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factor 49(y-4)^2-9(y+2)^2

factor

49 (y - 4)^{2} - 9 (y + 2)^{2}

4 (5 y - 11) (2 y - 17)

Solution steps

49 (y - 4)^{2} - 9 (y + 2)^{2}

49 (y - 4)^{2} = (7 (y - 4))^{2}

9 (y + 2)^{2} = (3 (y + 2))^{2}

= (7 (y - 4))^{2} - (3 (y + 2))^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

(7 (y - 4))^{2} - (3 (y + 2))^{2} = (7 (y - 4) + 3 (y + 2)) (7 (y - 4) - 3 (y + 2))

= (7 (y - 4) + 3 (y + 2)) (7 (y - 4) - 3 (y + 2))

Simplify

(7 (y - 4) + 3 (y + 2)) (7 (y - 4) - 3 (y + 2)) : (10 y - 22) (4 y - 34)

= (10 y - 22) (4 y - 34)

Factor

10 y - 22 : 2 (5 y - 11)

Factor

4 y - 34 : 2 (2 y - 17)

= 2 (5 y - 11) \cdot 2 (2 y - 17)

Multiply the numbers:

2 \cdot 2 = 4

= 4 (5 y - 11) (2 y - 17)

- 2 \times (- \frac{1}{2})

5 \frac{19}{25}

8 \div 1 \frac{4}{5}

\frac{6}{20}

(x - 2) \times (x + 3)

What is factor 49(y-4)^2-9(y+2)^2 ?
The solution to factor 49(y-4)^2-9(y+2)^2 is 4(5y-11)(2y-17)