Math, asked by Hitesh9691, 3 days ago

class 9th
verify a³+b³= (a+b)(a²-ab+b²)

Answers

Answered by preeti353615

Answer:

a³+b³= (a+b)(a²-ab+b²)

Step-by-step explanation:

verify a³+b³= (a+b)(a²-ab+b²)

RHS= (a + b) (a² - ab + b²)

= a(a² - ab + b²) + b(a² - ab + b²)

= a(a²) - a(ab) + a(b²) + b(a²) - b (ab) + b(b²)

= a³ - a²b + ab² +a²b - ab² + b³

Rearrange similar terms

= a³ - a²b +a²b + ab² - ab² + b³

= a³+b³

= LHS

a³+b³= (a+b)(a²-ab+b²)

Hence verified.

Answered by manomya

Answer:

n in Figure 5.1(c). The stack in Figure 5.1(c) forms Arrangement 1. The total volume of this arrangement of cubes is calculated (see the calculations).

Math Labs with Activity - Verify the Identity a³ - b³ =(a-b)(a² + ab+b²) 1

Step 2: We shall make Arrangement 2 for 26 cubes.

This arrangement consists of three stacks—the first stack [shown in Figure 5.2(a)] consists of 9 columns of two cubes each, the second stack [shown in Figure 5.2(b)] consists of two rows of three cubes each, and the third stack consists of 1 row of 2 cubes.

The total volume of this arrangement of cubes is calculated (see the calculations).

Math Labs with Activity - Verify the Identity a³ - b³ =(a-b)(a² + ab+b²) 2

Observations

Since the two arrangements have equal number of cubes (each arrangement has 26 cubes) and all the cubes have the same volume (1 cubic unit), the total volumes in both the arrangements must be equal.

Calculations

Volume of Arrangement 1

Volume of the stack in Figure 5.1(a) = a³.

Volume of the stack in Figure 5.1(b) =b³.

=volume of Arrangement 1 volume of the stack in Figure 5.1(c)

= volume of the stack in Figure 5.1(a)

=volume of the stack in Figure 5.1(b) = a³-b³.

Volume of Arrangement 2

Volume of the stack in Figure 5.2(a)=(a-b)a².

Volume of the stack in Figure 5.2(b) =(a-b)ab.

Volume of the stack in Figure 5.2(c) = (a-b)b².

volume of Arrangement 2 = (a-b)a² + (a -b)ab + (a -b)b².

=(a-b)(a² + ab+b²).

Since the total volume in the two arrangements must be the same, therefore

a³ – b³ =(a-b)(a² + ab+b²).

Result

It is verified that a³ – b³ =(a-b)(a² + ab+b²).

Remarks: The students must try to verify this identity for other values of a and b by taking required number of cubes and arranging them suitably.

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class 9thverify a³+b³= (a+b)(a²-ab+b²)​

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class 9th
verify a³+b³= (a+b)(a²-ab+b²)