Question

solve these questions​

Answer 1

$(i) (x²-5)(x+5)+25$

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

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

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

$(ii)( a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)$

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

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

$= > (1 + 1 + 2)ac + ( - 1 + 1)ad + (1 - 1)bc + ( - 1 - 1 + 2)bd$

$= > 4ac + (0)ad + (0)(bc) + (0)bd = 4ac + 0 + 0$

$= > 4ac$

$(iii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y$

$= > (1.5x)(1.5x) + (1.5x)(4y) + (1.5x)(3)- (4y)(1.5x) -(4y)(4y) - 4y \times 3 - 4.5x + 12y$

$= > {2.25x}^{2} + 6xy + 4.5x - 6xy - {16y}^{2} - 12y - 4.5x + 12y$

$= > {2.25x}^{2} - {16y}^{2}$

I hope this will help you dear..

Always stay safe and stay healthy..

Answer 2

Question No.1:-

(x² - 5) (x + 5) + 25

Answer:-

=> x³ + 5x² - 5x

How To Get It:-

=> x²(x + 5) - 5(x + 5) + 25

=> x³ + 5x² - 5x - 25 + 25

=> x³ + 5x² - 5x

✓Solved_

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Question No.2:-

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

Answer:-

=> 4ac

How To Get It:-

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

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

=> ac + ac - bd - bd + 2ac + 2bd

=> 2ac - 2bd + 2ac + 2bd

=> 4ac

✓Solved_

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Question No.3:-

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

Answer:-

=> 2.25x² - 16y²

How To Get It:-

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

=> 2.5x² + 6xy + 4.5x - 6xy - 16y² - 12y - 4.5x + 12y

=> 2.25x² - 16y²

✓Solved_

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Point To Be Noted:-

All The Above Problems Are Solved By Using The Distributive Property Of Multiplication.

$\: \: \:$

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