Note: This is the Solution of review exercise 4.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 4.2
Question # 01: Factorize each of the following expressions:
\((i)\) \(\quad\) \( 4x^4+81y^4\)
\((ii)\) \(\quad\) \(a^4+64b^4\)
\((iii)\) \(\quad\) \(x^4+4x^2+16 \)
\((iv)\) \(\quad \)\(x^4-14x^2+1 \)
\((v)\) \(\quad \) \(x^4-30x^2y^2+9y^4 \)
\((vi)\) \(\quad \) \(x^4+11x^2y^2+y^4\)
Question 2: Factorize each of the following expresssions:
\((i)\) \(\quad\) \( (x+1)(x+2)(x+3)(x+4)+1\)
\((ii)\) \(\quad\) \((x+2)(x-7)(x-4)(x-1)+17\)
\((iii)\) \(\quad\) \((2x^2+7x+3)(2x^2+7x+5)+1 \)
\((iv)\) \(\quad \)\((3x^2+5x+3)(3x^2+5x+5)-3 \)
\((v)\) \(\quad \)\((x+1)(x+2)(x+3)(x+6)-3x^2 \)
\((vi)\) \(\quad \)\((x+1)(x-1)(x+2)(x-2)+13x^2 \)
Question 3: Factorize:
\((i)\) \(\quad\) \( 8x^3+12x^2+6x+1\)
\((ii)\) \(\quad\) \(27a^3+108a^2b+144ab^2+64b^3\)
\((iii)\) \(\quad\) \(x^3+48x^2y+108xy^2+216y^3 \)
\((iv)\) \(\quad \)\(8x^3-125y^3+150xy^2-60x^2y \)
Question 4: Factorize:
\((i)\) \(\quad\) \( 125a^3-1\)
\((ii)\) \(\quad\) \(64x^3+125\)
\((iii)\) \(\quad\) \(x^6-27 \)
\((iv)\) \(\quad \)\(1000a^3+1 \)
\((v)\) \(\quad \) \(343x^3+216 \)
\((vi)\) \(\quad \) \(27-512y^3 \)