Question

please give me answer.​

Answer 1

${\Huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Solve:

1. $(x + y)^2$
2. $(p + 6)^2$
3. $(2a - b)^2$
4. $(5l - 2m)^2$
5. $9r^2 - 4s^2$
6. $(3s + 5t)^2$
7. $(x - 6y)^2$
8. $9m - 16n$
9. $(5a + 7b)^2$
10. $(4x - 6y)^2$

Solution:

$1) (x + y)^2$

$:\implies (x + y)^2 \\:\implies (x)^2 + 2(x)(y) + (y)^2 \\\bf{:\implies x^2 + 2xy + y^2}$

$2) (p + 6)^2$

$:\implies (p + 6)^2 \\:\implies (p)^2 + 2(p)(6) + (6)^2 \\\bf{:\implies p^2 + 12p + 36}$

$3) (2a - b)^2$

$:\implies (2a - b)^2 \\:\implies (2a)^2 - 2(2a)(b) + (b)^2 \\\bf{:\implies 4a^2 - 4ab + b^2}$

$4) (5l - 2m)^2$

$:\implies (5l - 2m)^2 \\:\implies (5l)^2 - 2(5l)(2m) + (2m)^2 \\\bf{:\implies 25l^2 - 20ml + 4m^2}$

$5) 9r^2 - 4s^2$

$:\implies 9r^2 - 4s^2 \\:\implies (3r)^2 - (2s)^2 \\\bf{:\implies (3r - 2s)(3r + 2s)}$

$6) (3s + 5t)^2$

$:\implies (3s + 5t)^2 \\:\implies (3s)^2 + 2(3s)(5t) + (5t)^2 \\\bf{:\implies 9s^2 + 30st + 25t^2}$

$7) (x - 6y)^2$

$:\implies (x - 6y)^2 \\:\implies (x)^2 - 2(x)(6y) + (6y)^2 \\\bf{:\implies x^2 - 12xy + 36y^2}$

$8) 9m - 16n$

$:\implies 9m - 16n \\:\implies (3\sqrt{m})^2 - (4\sqrt{n})^2 \\\bf{:\implies (3\sqrt{m} - 4\sqrt{n})(3\sqrt{m} + 4\sqrt{n})}$

$9) (5a + 7b)^2$

$:\implies (5a + 7b)^2 \\:\implies (5a)^2 + 2(5a)(7b) + (7b)^2 \\\bf{:\implies 25a^2 + 70ab + 49b^2}$

$10) (4x - 6y)2$

$:\implies 2(4x) - 2(6y) \\\bf{:\implies 8x - 12y}$

Formula Used:

• $(a+b)^2 = a^2 + 2ab + b^2$
• $(a-b)^2 = a^2 - 2ab + b^2$
• $a^2 - b^2 = (a+b)(a-b)$

Learn More:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\bf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\bf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\8)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\9)\bf\: A^{3} - B^{3} = (A-B)(A^{2} + AB + B^{2})\\\\ \end{minipage}}$

Hope it helps!!!