Complete the table. First expressionSecond expressionProduct(i)ab+c+d(ii)x+y-55xy(iii)p6 p^2-7 p+5(iv)4 p^2 q^ 2 p^2-q^2(v)a+b+cabc

(i) a(b+c+d)=a b+a c+a d=a b+a c+a d (ii) (x+y-5) 5 x y=5 x y (x+y-5) [by commutative law] =(5 x y) (x)+(5 x y) (y)+(5 x y) (-5) =5 x^2 y+5 x y^2-25 x y (iii) p (6 p^2-7 p+5 ) =(p) (6 p^2 )+(p) (-7 p)+(p) 5 =6 p^3-7 p^2+5 p (iv) (4 p^2 q^2 ) (p^2-q^2 )= (4 p^2 q^2 ) (p)^2- (4 p^2 q^2 ) q^2 =4 p^4 q^2-4 p^2 q^4 (v) (a+b+c) a b c=a b c (a+b+c) [by commutative law] =(a b c) (a)+(a b c) (b)+(a b c) (c) =a^2 b c+a b^2 c+a b c^2

Complete the table. First expressionSecond expressionProduct(i)ab…

Download App

Question

Complete the table.

	First expression	Second expression	Product
(i)	$a$	$b+c+d$
(ii)	$x+y-5$	$5xy$
(iii)	$p$	$6 p^2-7 p+5$
(iv)	$4 p^2 q^{2}$	$p^2-q^2$
(v)	$a+b+c$	$abc$

✓

Answer

(i) $a(b+c+d)=a \times b+a \times c+a \times d=a b+a c+a d$
(ii) $(x+y-5) \times 5 x y=5 x y \times(x+y-5)\qquad$ [by commutative law]
$=(5 x y) \times(x)+(5 x y) \times(y)+(5 x y) \times(-5)$
$=5 x^2 y+5 x y^2-25 x y$
(iii) $p\left(6 p^2-7 p+5\right) =(p) \times\left(6 p^2\right)+(p) \times(-7 p)+(p) \times 5 $
$=6 p^3-7 p^2+5 p$
(iv) $\left(4 p^2 q^2\right) \times\left(p^2-q^2\right)=\left(4 p^2 q^2\right) \times(p)^2-\left(4 p^2 q^2\right) \times q^2 $
$=4 p^4 q^2-4 p^2 q^4$
(v) $(a+b+c) \times a b c=a b c \times(a+b+c)\qquad$ [by commutative law]
$=(a b c) \times(a)+(a b c) \times(b)+(a b c) \times(c) $
$ =a^2 b c+a b^2 c+a b c^2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Algebraic Expressions and Identities→Algebraic Expressions and Identities — all question types→MATHS STD 8 question papers→Gujarat Board STD 8 question papers→Gujarat Board question paper generator→

Similar questions

Factorise the following expressions.
(i) $a x^3-b x^2+c x$
(ii) $x^3 y^2+x^2 y^3-x y^4+x y$
(iii) $a^3+a^2+a+1$
(iv) $a x^2 y-b x y z-a x^2 z+b x y^2$

→

A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures $44\ cm \times 33\ cm$.

→

The marks obtained (out of 20) by 30 students of a class in a test are given below: $7, 10, 8, 16, 13, 14, 15, 11, 18, 11, 15, 10, 7, 14,$ $20, 19, 15, 16, 14, 20, 10, 11, 14, 17, 13, 12, 15, 14, 16, 17.$ Prepare a frequency distribution table for the above data using class intervals of equal width in which one class interval in $3-8$ (including $2$ and excluding $8$). From the frequency distribution table so obtained, draw a histogram.

→

The following table shows the percentage of students who dropped out of school after completing high school.

Age (in Year)	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$	$16$	$17$	$18$
Boys	$72\%$	$75\%$	$78\%$	$81\%$	$84\%$	$88\%$	$92\%$	$95\%$	$98\%$	$99\%$	$100\%$
Girls	$77\%$	$81\%$	$84\%$	$88\%$	$91\%$	$95\%$	$98\%$	$99\%$	$99.5\%$	$100\%$	$100\%$