Question

factorize 25x^2-4y^2+28yz-49z^2​

Answer 1

Answer:

(5x+2y-7z)(5x-2y+7z)

Step-by-step explanation:

25x²-4y²+28yz-49z²

= 25x²-(4y²-28yz+49z²)

= 25x² - [(2y)²-2×2y×7z+(7z)²]

= (5x)² - (2y-7z)²

/* By algebraic identity:

a²-2ab+b² = (a-b)² */

= [5x+(2y-7z)][5x-(2y-7z)]

/* By algebraic identity:

a²-b² = (a+b)(a-b) */

= (5x+2y-7z)(5x-2y+7z)

Therefore,

25x²-4y²+28yz-49z²

=(5x+2y-7z)(5x-2y+7z)

•••♪

Answer 2

(5x + 2y - 7z) (5x - 2y + 7z)

Step-by-step explanation:

Given,

25 $x^{2}$ - 4 $y^{2}$ + 28 yz - 49 $z^{2}$

Grouping the expressions:

25 $x^{2}$ - (4 $y^{2}$ - 28 yz + 49 $z^{2}$)

25 $x^{2}$ - ( (2y$)^{2}$ - (2 × 2y × 7z) + (7z$)^{2}$)

Applying the formula: $a^{2}$ - 2ab + $b^{2}$ = (a-b$)^{2}$

25 $x^{2}$ - (2y - 7z$)^{2}$

(5x$)^{2}$  - (2y - 7z$)^{2}$

Applying the formula: $a^{2}$ - $b^{2}$ = (a+b) (a-b)

(5x + (2y - 7z)) (5x - (2y - 7z))

(5x + 2y - 7z) (5x - 2y + 7z)

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