Question

1. Construct New Algebraic Expressions

Description: Fill in the gaps.

Algebraic Expression:

7ab+2a²+5b²

Terms

Factors

Apply Operator

New Terms

2

xb

xab

xb

xb

Multiply all the new terms 7x2x5xa x b

Answer:​

Answer 1

Answer:

1. Construct New Algebraic Expressions

Description: Fill in the gaps.

Algebraic Expression:

7ab+2a²+5b²

Terms

Factors

Apply Operator

New Terms

2

xb

xab

xb

xb

Multiply all the new terms 7x2x5xa x b

Answer:answer mark as brainlist please

Answer 2

Answer:

The algebraic equation $7ab + 2a^{2} +5 b^{2}$  can be factorised into following  linear algebraic factors

=  $(a+b) ( 2a+5b)$.

Step-by-step explanation:

STEP 1 :

• Let us consider the algebraic equation :

              $= 2a^{2} + 5b^{2} +7ab$

• The algebraic equation can be re-written as ,

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

STEP 2 :

• Grouping the terms  $a^{2} ,b^{2} ,2ab$  to form a perfect square.

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

• Using the identity   $(a+b)^{2} = a^{2} +b^{2} +2ab$

      $= (a+b)^{2} + (a+b)^{2} + 3b^{2} + 3ab$

      $= 2(a+b)^{2} + 3b^{2} + 3ab$

STEP 3 :

• Taking  $3b$  common from  $(3b^{2} +3ab)$ .

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

          $= 2(a+b)^{2} +3b(a+b)$

Taking $(a+b)$ as common factor from above formed equation,

• $=(a+b) [ 2(a+b) + 3b]$

• = $(a+b) [ 2a+ 2b + 3b ]$

• $= (a+b) (2a+5b)$

The final answer is $(a+b) (2a+5b)$ .

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