**NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.4 – Algebraic Expressions & Identities**

**NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.4 – Algebraic Expressions & Identities, has been designed by the NCERT to test the knowledge of the student on the topic – Multiplying a Polynomial by a Polynomial**

- Multiplying a binomial by a binomial
- Multiplying a binomial by a trinomial

**Q.1 Multiply the binomials.**

**(i)(2x+5)and(4x−3)**

**(ii)(y−8)and(3y−4)**

**(iii)(2.5l−0.5m)and(2.5l+0.5m)**

**(iv)(a+3b)and(x+5)**

**(v)(2pq+3q²)and(3pq−2q²)**

**(vi)**

**Answer:**

**i.**

**ii.**

**iii.**

**iv. **

**v. **

**vi. **

**Q.2 ****Find the product. **

**i. (5 – 2****x****) (3 + ****x****)
**

**ii. (**

**x**

**+ 7**

**y**

**) (7**

**x**

**–**

**y**

**)**

**iii. (**

**a**

^{2}**+**

**b**

**) (**

**a**

**+**

**b**

^{2}**)**

**iv. (**

**p**

^{2}**–**

**q**

^{2}**) (2**

**p**

**+**

**q**

**)**

**i.** (5-2x)(3+x)=5(3+x)-2x(3+x)

= 15+5x-6x-2x^{2
}=15-x-2x^{2}

**ii.** (x + 7y) (7x – y)

= x (7x – y) + 7y (7x – y)

= 7x^{2} – xy + 49xy – 7y^{2
}= 7x^{2}+48xy-7y^{2}

**iii.** (a^{2}+b)(a+b^{2})

= a^{2} (a+b^{2})+b(a+b^{2})

=a^{3}+a^{2}b^{2}+ab+b^{3}

**iv.** (p^{2}-q^{2})(2p+q)

=p^{2} (2p+q)-q^{2}(2p+q)

=2p^{3}+p^{2}q-2pq^{2}-q^{3}

**Q.3 Simplify. **

**i. (****x**^{2}** – 5) (****x**** + 5) + 25
**

**ii. (**

**a**

^{2}**+ 5) (**

**b**

^{3}**+ 3) + 5**

**iii. (**

**t**

**+**

**s**

^{2}**) (**

**t**

^{2}**– s)**

**iv. (**

**a**

**+**

**b**

**) (**

**c**

**–**

**d**

**) + (**

**a**

**–**

**b**

**) (**

**c**

**+**

**d**

**) + 2 (**

**ac**

**+**

**bd**

**)**

**v. (**

**x**

**+**

**y**

**) (2**

**x**

**+**

**y**

**) + (**

**x**

**+ 2**

**y**

**) (**

**x**

**–**

**y**

**)**

**vi. (**

**x**

**+**

**y**

**) (**

**x**

^{2}**–**

**xy**

**+**

**y**

^{2}**)**

**vii. (1.5**

**x**

**– 4**

**y**

**) (1.5**

**x**

**+ 4**

**y**

**+ 3) – 4.5**

**x**

**+ 12**

**y**

**viii. (**

**a**

**+**

**b**

**+**

**c**

**) (**

**a**

**+**

**b**

**–**

**c**

**)**

**Solution:**

**i.** (x^{2}-5)(x+5)+25

= x^{2} (x+ 5)-5(x+5)+25

= x^{3}+5x^{2}-5x-25+25

= x^{3}+5x^{2}-5x

**ii.** (a^{2}+5)(b^{3}+3)+5

= a^{2}(b^{3}+3)+5(b^{3}+3)+5

= a^{2}b^{3}+3a^{2}+5b^{3}+15+5

= a^{2}b^{3}+3a^{2}+5b^{3}+20

**iii.** (t+s^{2})(t^{2}-s)

= t(t^{2}-s)+s^{2}(t^{2}-s)

= t^{3}-st+s^{2}t^{2}-s^{3}

**iv.** (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)

=a(c-d)+b(c-d)+a(c+d)-b(c+d)+2(ac+bd)

=ac-ad+bc-bd+ac+ad-bc-bd+2ac+2bd

=4ac

**v.** (x+y)(2x+y)+(x+2y)(x-y)

=x(2x+y)+y(2x+y)+x(x-y)+2y(x-y)

=2x²+xy+2xy+y²+x²-xy+2xy-2y²

=3x²-y²+4xy

**vi.** (x+y)(x2-xy+y2)

=x(x²-xy+y²)+y(x²-xy+y²)

=x³-x²y+xy²+x²y-xy²+y³

=x³+y³

**vii.** (1.5x-4y)(1.5x+4y+3)-4.5x+12y

=1.5x(1.5x+4y+3)-4y (1.5x+4y+3)-4.5x+12y

=2.25x²+6xy+4.5x-6xy-16y²-12y-4.5x+12y

=2.25x²-16y²

**viii.** (a+b+c)(a+b-c)

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

=a²+ab-ac+ab+b²-bc+ca+bc-c²

=a²+b²-c²+2ab

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.5 – Algebraic Expressions and Identities can be accessed by clicking here**

**NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.4 – Algebraic Expressions & Identities**

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