Question

Factorize
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Answer 1

Step-by-step explanation:

10) take (a+b) as 'k', you'll get a quadratic equation. Factorise it.

Similarly for all problems

b) take p+q as k

11) take x-2y as k

b) take 2x-3y as k

Answer 2

Solution:

10.

i) Let, a + b = x

So, the equation is ... x²- 11x - 42

[by splitting middle term]

x² - 14x + 3x - 42

x(x - 14) + 3(x - 14)

(x + 3)(x - 14)

[putting the value of x]

(a + b + 3)(a + b - 14)

ii) Let, p + q = m

So, the equation is..... 8 + 6m - 5m²

[by splitting middle term]

8 + 10m - 4m -5m²

2(4 + 5m) - m(4 + 5m)

(2 - m)(4 + 5m)

[putting the value of m]

[2 - (p + q)][4 + 5(p+ q)]

(2 - p - q)(4 + 5p + 5q)

11.

i) let, x - 2y = a

So, the equation is ... a² - 6a + 5

[by splitting middle term]

a² - 5a - a + 5

a(a - 5) - 1(a - 5)

(a - 5)(a - 1)

[putting the value of a ]

(x - 2y - 5)(x - 2y - 1)

ii) Let, 2x - 3y = k

So, the equation is ..... 7 + 10k - 8k²

[by splitting middle term]

7 + 14k - 4k - 8k²

7(1 + 2k) - 4k( 1 + 2k)

(1 + 2k)(7 - 4k)

[ putting the value of k ]

[1 + 2(2x - 3y)][7 - 4(2x - 3y)]

(1 + 4x - 6y)(7 - 8x + 12y)