Factorise : 2(ab + cd) - a 2 - b 2 + c 2 + d 2

Given, 2(ab + cd) - a 2 - b 2 + c 2 + d 2 = 2ab + 2cd - a 2 - b 2 + c 2 + d 2 = c 2 + d 2 + 2cd - (a 2 + b 2 - 2ab) = (c + d) 2 - (a - b) 2 = (c + d + a - b)[c + d - (a - b)] = (c + d + a - b)(c + d - a + b). Hence, 2(ab + cd) - a 2 - b 2 + c 2 + d 2 = (c + d + a - b)(c + d - a + b).

Mathematics

Factorise :
2(ab + cd) - a² - b² + c² + d²

Factorisation

6 Likes

Answer

Given,

2(ab + cd) - a² - b² + c² + d²

= 2ab + 2cd - a² - b² + c² + d²

= c² + d² + 2cd - (a² + b² - 2ab)

= (c + d)² - (a - b)²

= (c + d + a - b)[c + d - (a - b)]

= (c + d + a - b)(c + d - a + b).

Hence, 2(ab + cd) - a² - b² + c² + d² = (c + d + a - b)(c + d - a + b).

Answered By

3 Likes

Mathematics

Factorise :
2(ab + cd) - a² - b² + c² + d²

Factorisation

Answer

Related Questions

Evaluate :
$\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}$

Factorise :
9x² + 3x - 8y - 64y²

Factorise :
$2\sqrt{3}x^2 + x - 5\sqrt{3}$

Factorise :
$\dfrac{1}{4}(a + b)^2 - \dfrac{9}{16}(2a - b)^2$

Mathematics

Factorise :2(ab + cd) - a2 - b2 + c2 + d2

Factorisation

Answer

Related Questions

Evaluate :5.67×5.67×5.67+4.33×4.33×4.335.67×5.67−5.67×4.33+4.33×4.33\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}5.67×5.67−5.67×4.33+4.33×4.335.67×5.67×5.67+4.33×4.33×4.33​

Factorise :9x2 + 3x - 8y - 64y2

Factorise :23x2+x−532\sqrt{3}x^2 + x - 5\sqrt{3}23​x2+x−53​

Factorise :14(a+b)2−916(2a−b)2\dfrac{1}{4}(a + b)^2 - \dfrac{9}{16}(2a - b)^241​(a+b)2−169​(2a−b)2

Factorise :
2(ab + cd) - a² - b² + c² + d²

Evaluate :
$\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}$

Factorise :
9x² + 3x - 8y - 64y²

Factorise :
$2\sqrt{3}x^2 + x - 5\sqrt{3}$

Factorise :
$\dfrac{1}{4}(a + b)^2 - \dfrac{9}{16}(2a - b)^2$