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Factor using suitable identities: 9a square + 4b square + c square – 12ab + 6ac – 4bc
To factor this six-term polynomial, we look at the signs of the products to determine which base is negative. The perfect square bases are 3a, 2b and c. We notice that the terms 12ab and 4bc are negative, while 6ac is positive. Since the negative terms both contain the variable b, the base associateRead more
To factor this six-term polynomial, we look at the signs of the products to determine which base is negative. The perfect square bases are 3a, 2b and c. We notice that the terms 12ab and 4bc are negative, while 6ac is positive. Since the negative terms both contain the variable b, the base associated with b must carry the negative sign. This results in the factor (3a – 2b + c) square.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
See lessExpand using the identity (a + b + c) square: (p + 3q + 7r) square
We use the three-term square identity to expand the given expression. By setting a equal to p, b equal to 3q and c equal to 7r, we square each term to get p square, 9q square and 49r square. Then we calculate the three double cross-product terms: two times p times 3q gives 6pq; two times 3q times 7rRead more
We use the three-term square identity to expand the given expression. By setting a equal to p, b equal to 3q and c equal to 7r, we square each term to get p square, 9q square and 49r square. Then we calculate the three double cross-product terms: two times p times 3q gives 6pq; two times 3q times 7r gives 42qr; two times 7r times p gives 14rp. Combining them gives the full expansion.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
See lessExpand using the identity (a + b + c) square: (3x – 2y + 4z) square
We expand this expression using the three-term standard identity. Here, our terms are 3x, minus 2y and 4z. Squaring these individual parts results in 9x square, 4y square and 16z square. When calculating the paired products, any term multiplied by minus 2y becomes negative, resulting in minus 12xy aRead more
We expand this expression using the three-term standard identity. Here, our terms are 3x, minus 2y and 4z. Squaring these individual parts results in 9x square, 4y square and 16z square. When calculating the paired products, any term multiplied by minus 2y becomes negative, resulting in minus 12xy and minus 16yz. The final product two times 4z times 3x stays positive at 24zx.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
See lessIs this an identity? (a + b – c) square + (a – b + c) square + (a – b – c) square = 2a square + 2b square + 2c square
To check if this equation is an identity, we must expand all three squared brackets on the left side using the three-term formula. Summing the expanded terms together results in a total of 3a square + 3b square + 3c square minus 2ab minus 2bc minus 2ca. Since this long combined expression is completRead more
To check if this equation is an identity, we must expand all three squared brackets on the left side using the three-term formula. Summing the expanded terms together results in a total of 3a square + 3b square + 3c square minus 2ab minus 2bc minus 2ca. Since this long combined expression is completely different from the given right-hand side of 2a square + 2b square + 2c square, the equation is not an identity.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
See lessFill in the blanks to complete the following identities: s square – 11s + 24 = () ()
To complete this quadratic identity without using tiles, we compare it to the standard form x square + (a + b)x + ab. We look for two integers, a and b, whose sum equals minus 11 and whose product equals 24. The numbers that satisfy both equations are minus 3 and minus 8. Substituting these into theRead more
To complete this quadratic identity without using tiles, we compare it to the standard form x square + (a + b)x + ab. We look for two integers, a and b, whose sum equals minus 11 and whose product equals 24. The numbers that satisfy both equations are minus 3 and minus 8. Substituting these into the factored form results in the final blank answers of (s – 3) and (s – 8).
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 4 Exploring Algebraic Identities (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-4/
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