Here we will solve different types of Problems on Factorization by grouping of terms.
1. Factorize: a^{2} – (b – 5)a – 5b.
Solution:
Given expression = a^{2} – (b – 5)a – 5b
= a^{2} – ba + 5a – 5b
= a(a - b) + 5(a - b)
= (a – b)(a + 5).
2. Factorize: a^{2} + b^{2} + a + b + 2ab
Solution:
Given expression = a^{2} + b^{2} + a + b + 2ab
= a^{2} + 2ab + b^{2} + (a + b)
= (a + b)^{2} + (a + b)
= (a + b){(a + b) + 1}
= (a + b)(a + b + 1).
3. Find the factors by grouping of terms: x^{2} – 2x – 2y + xy
Solution:
Given expression = x^{2} – 2x – 2y + xy
= x^{2} – 2x + xy – 2y
= x(x – 2) + y(x – 2)
= (x – 2)(x + y).
Therefore, the factors are x – 2 and x + y.
4. Factorize: 5x^{3} – 15x^{2} – x + 3
Solution:
Given expression = 5x^{3} – 15x^{2} – x + 3
= 5x^{2}(x – 3) – 1(x – 3)
= (x – 3)(5x^{2} – 1)
5. Factorize by grouping: x^{2} – (a + 4)x + 4a
Solution:
Given expression = x^{2} – (a + 4)x + 4a
= x^{2} – ax – 4ax + 4a
= x(x – a) – 4a(x – a)
= (x – a)(x – 4a)
From Problems on Factorization by Grouping of Terms to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Sep 17, 24 02:25 AM
Sep 17, 24 01:47 AM
Sep 17, 24 12:10 AM
Sep 16, 24 11:24 PM
Sep 16, 24 02:40 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.