Exercise 12.2
1. Factorise the following expressions.
(iv)
- The above identity is in the form of the identity:
where a and b are two integers. - Thus, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
(vi)
- The above identity is in the form of the identity:
where a and b are two integers. - Thus, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
(vii)
- Expand the first term using the identity
- Upon simplifying, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
(viii)
- Upon simplifying using the identity, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
2. Factorise.
(ii)
- Take out the common factor of
which gives us the form: a 2 − b 2 - Upon simplifying using the identity, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
(iv)
- Take out the common factor of
which gives us the form: a 2 − b 2 - Upon simplifying using the identity, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
(v)
- Upon expanding and simplifying using the identity, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
(vii)
- Upon simplifying using the identities, the resulting factorised form becomes
- So, we get the following
- Which gives us the above factorised answer
(viii)
- We observe that the
three terms are together form an identity. - Upon simplifying using the identities, the resulting factorised form becomes
- So, we get the following
- Further on
- Which gives us the above factorised answer
3. Factorise the expressions.
(ii)
- Upon simplifying using the identities, the resulting factorised form becomes
- So, we get the following as the factorised answer, upon taking the common factor.
(v) (lm + l) + m + 1
- Upon simplifying using the identities, the resulting factorised form becomes
- Further on
- So, we get the following as the factorised answer
(vi) y(y + z) + 9(y + z)
- Upon simplifying using the identities, the resulting factorised form becomes
- So, we get the following as the factorised answer
(vii)
- Upon simplifying using the identities, the resulting factorised form becomes
- Upon simplifying
- We get the factorised answer
(viii) 10ab + 4a + 5b + 2
- Upon simplifying using the identities, the resulting factorised form becomes
- Upon simplifying
- We get the factorised answer
4. Factorise.
(iii)
- Upon simplifying using the identities, the resulting factorised form becomes
- Upon simplifying
- Further expanding using identities
- More over we get
- We get the factorised answer
(iv)
- Upon simplifying using the identities, the resulting factorised form becomes
- Upon simplifying
- Further expanding using identities
- More over we get
- We get the factorised answer
(v)
- Upon simplifying using the identities, the resulting factorised form becomes
- Upon simplifying
- Further expanding using identities
- More over we get
- We get the factorised answer
5. Factorise the following expressions.