In this page we have Class 8 maths exercise 8.4 solutions for
Algebraic Expressions .This exercise has questions about multiplication of polynomials by polynomials. Hope you like them and do not forget to like , social share
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Class 8 maths exercise 8.4 solutions

Question 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 + 3q^{2}) and (3pq – 2q^{2}) Answer:
Let ( a+b) (c+d) to be done
then
(a+b) (c+d)= a(c+d) + b( c+d)
=a x c+a x d+b x c+b x d

We will use the same concept in all the question below
(i) (2x + 5)(4x - 3)
= 2x x 4x - 2x x 3 + 5 x 4x - 5 x 3
= 8x² - 6x + 20x -15
= 8x² + 14x -15
(ii) ( y - 8)(3y - 4)
= y x 3y - 4y - 8 x 3y + 32
= 3y^{2} - 4y - 24y + 32
= 3y^{2} - 28y + 32
(iii) (2.5l - 0.5m)(2.5l + 0.5)
Using (a+b)(a-b) = a^{2} - b^{2}
We get = 6.25l^{2} - 0.25m^{2}
(iv) ax + 5a + 3bx + 15b
v) 2pq x 3pq - 2pq x 2q^{2} + 3q^{2}x 3pq - 3q^{2}x 2q^{2}
= 6p^{2}q^{2} - 4pq^{3} + 9pq^{3} - 6q^{4}
= 6p^{2}q^{2} - 5pq^{3} - 6p^{4}

Question 2
Find the product.
(i) (5 – 2x) (3 + x)
(ii) (x + 7y) (7x – y)
(iii) (a^{2}+ b) (a + b^{2})
(iv) (p^{2}– q^{2}) (2p + q) Answer:
(i) 15 + 5x - 6x - 2x^{2}
= 15 - x - x ^{2}
(ii) 7x^{2} - xy + 49xy - 7y^{2}
= 7x^{2} - 7y^{2} + 48xy
(iii) a^{2} x a + a^{2 }x b + a x b + b^{3}
= a^{3} + a^{2}b + ab + b^{3}
= a^{3} + b^{3} + a^{2}b + ab
(iv) 2p^{3} + p^{2}q - 2pq^{2} - q^{3}
= 2p^{3} - q^{3} + p^{2}q - 2pq^{2}

Question 3
Simplify.
(i) (x^{2}– 5) (x + 5) + 25
(ii) (a^{2}+ 5) (b^{3}+ 3) + 5
(iii) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
(iv) (x + y)(2x + y) + (x + 2y)(x – y)
(v) (x + y)(x^{2}– xy + y^{2})
(vi) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
(vii) (a + b + c)(a + b – c) Answer:
(i) x^{3} + 5x^{2} - 5x - 25 + 25
= x3 + 5x^{2} -5x
(ii) a^{2}b^{3} + 3a^{2} + 5b^{3} + 15 + 5
= a^{2}b^{3} + 5b^{3} + 3a^{2} + 20
(iii) (ac - ad + bc - bd) + (ac + ad - bc - bd) + (2ac + 2bd)
= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd
= 4ac
(iv) 2x^{2} + xy + 2xy + y^{2} + x^{2} - xy + 2xy - 2y^{2}
= 3x^{2} + 4xy - y^{2}
(v) x^{3} - x^{2}y + xy^{2} + x^{2}y - xy^{2} + y^{3}
= x^{3} + y^{3}
(vi) 2.25x^{2} + 6xy + 4.5x - 6xy - 16y^{2} - 12y - 4.5x + 12y
= 2.25x^{2} - 16y^{2}
(vii) a^{2} + ab - ac + ab + b^{2} - bc + ac + bc - c^{2}
= a^{2} + b^{2} - c^{2} + 2ab

Summary

Class 8 maths exercise 8.4 solutions has been prepared by Expert with utmost care. If you find any mistake.Please do provide feedback on mail. You can download the solutions as PDF in the below Link also Download Algebraic Expressions Exercise 8.4 as pdf

This chapter 8 has total 4 Exercise 8.1 ,8.2 ,8.3 ,8.4 as per latest syllabus.Exercise 8.5 is deleted as per latest syllabus. This is the Fourth exercise in the chapter.You can explore previous exercise of this chapter by clicking the link below